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In this book, the author's goal is to provide an introduction to some of the analytic underpinnings for the geometry of anti-self duality in 4-dimensions. Anti-self duality is rather special to 4-dimensions and the imposition of this condition on curvatures of connections on vector bundles and on curvatures of Riemannian metrics has resulted in some spectacular mathematics. The book reviews some basic geometry, but it is assumed that the reader has a general background in differential geometry (as would be obtained by reading a standard text on the subject). Some of the fundamental references include Atiyah, Hitchin and Singer, Freed and Uhlenbeck, Donaldson and Kronheimer, and Kronheimer and Mrowka. The last chapter contains open problems and conjectures. ... Read more

Customer Reviews (2)

poorly written, very sloppy, with limited scope
First of all, don't pay too much heed to Dr. Carlson's review of this book, since he apparently didn't read more than a page or two (cf. my comment on his review). While much of the book discusses Donaldson's work on the moduli spaces of anti-self-dual connections over a closed 4-manifold, that isn't really the focus or purpose of this work. The real purpose is to (sort of) prove the following theorem on anti-self-dual (ASD) metrics (i.e., Riemannian metrics with zero self-dual Weyl curvature; W+ = 0):

Let M be a compact, oriented, 4-dimensional manifold (w/o boundary). Then there exists a positive integer N such that the connected sum of M with n copies of -CP^2 (i.e., 2-d complex projective space with the reverse orientation) has metrics with W+ = 0 for all n >= N.

So the author is interested in proving an existence theorem, one which bears much similarity to the earlier existence theorem ("Taubes's existence theorem") he provided for anti-self-dual connections on the same kinds of 4-manifolds, which was one of the key steps in Donaldson's theorem in gauge theory. Thus in this book Taubes first gives an overview of Donaldson theory (which is why Dr. Carlson was confused) and then sketches a (30-page) proof of its existence theorem. Afterward he returns to self-dual metrics, and provides another 30-page proof of the aforementioned main theorem, semi-modeled on the preceding one and involving many of the same analytic techniques. Finally he concludes with some open (at that time, and still open as far as I know) problems concerning self-dual metrics and Donaldson theory.

I say sketch because even though he devotes 30 pages to the proof, he doesn't quite succeed in proving it, having to refer to other papers at a number of points and making frequent errors. Infact, he botches the proof so badly (and shockingly, considering that it was his theorem!), I had to supply my own. He tries to make the proof easier to digest for novices by first considering several special cases and working up to the full generality, but he ends up repeating a number of statements and equations and even unnecessarily reproving things in different ways. What's worse is that some statements are in fact incorrect, such as eq'ns (4.26), (5.6), (5.4), and especially (5.27) and the condition derived for E immediately after it. I wrote a page of equations and attached it to p. 53 of the book to replace the disorganized mess that concludes the proof. Ironically, he made this proof much longer than the versions that appear in his original paper and in Freed & Uhlenbeck's Instantons and Four-Manifolds, Lawson's Theory of Gauge Fields in Four Dimensions, and Donaldson & Kronheimer's The Geometry of Four-Manifolds in an effort to appeal to students, and while this does have the advantage of making it easier to understand what he is trying to do, it also has the unfortunate result of seeing him fail to accomplish it.

The proof of the main theorem on ASD metrics suffers from many of the same deficiencies. While it is much longer, with more detail and background information, than the proof in his original papers, it also contains several serious errors and there are gaps where technical results are only stated but not proved. Most embarrassing are a statement on p. 72 where it is stated that a certain function is square integrable when it isn't and the equations (9.9) and (9.10), which are not only incorrect, but even if they weren't, still fail to provide an expression for Q-bar over the entire manifold in terms of Q. This latter point is so serious, it is unclear whether the theorem has even been proved - it will be necessary to consult the original papers.

The editing for the book is also virtually nonexistent; infact, I seriously doubt it was edited at all. Among the plethora of typos include "have" instead of "half," "a priori" spelled as one word on a number of occasions, and even more mysteriously "in fact" written as one word ("infact"), not once but a dozen times or more (I have done it twice in this review as an illustration). There are also problems with the references to theorems and equations (it seems that they were renumbered but the references weren't amended) and variables are often written in roman instead of italic font, which becomes a problem when the variable is an "a."

Despite all these demerits there are a few positives. First of all, the level is a little lower than most of his original papers, with definitions provided for such basic concepts as the connected sum, the Fredholm property, connections, and the contraction mapping theorem. Second, his explanations of how the theorems work, rather than the details, are valuable in introducing the beginner to gauge theory, which is notoriously difficult to learn. Third, the main theorem itself may be of interest to some differential geometers. Fourth, the problems in the final chapter, and even more significantly, the connections between ASD metrics and connections alluded to in the all-too-brief Chapter 6, although not relevant to the rest of the book, offer a glimpse into a potentially deeper and more fascinating theory, in which the Donaldson polynomials are encoded in twister spaces of manifolds with ASD metrics and in which knowledge of the moduli space of based ASD metrics leads to information about the group of orientation-preserving diffeomorphisms of a manifold.

Don't get me wrong - Taubes is a brilliant mathematician, one of the best in gauge theory; but this was far from his best work.

Out of date, but still could be useful
The results in this book have been superseded by the results of Nathan Seiberg and Edward Witten that appeared a short time after this book was published. The Seiberg-Witten theory caused great excitement among the mathematical community who do research in differential geometry and differential topology, particularly in the area of the differential toplogy of 4-dimensional manifolds. Proclaiming the "end of the Donaldson theory", mathematicians moved on to study the properties of the Seiberg-Witten equation, which is still nonlinear enough to be interesting.

Thus the discussions in this book are somewhat dated, but still could be of interest from a mathematical history standpoint or with the goal perhaps of motivating the Seiberg-Witten theory, although the self-dual Yang-Mills equations, a cornerstone of the Donaldson theory, are not discussed in the book. Instead the author studies the anti-self dual equations. These arise uniquely in four dimensions due to the fact thatthe Lie algebra so(4) of the special orthogonal group SO(4) is not simple, but instead decomposes as the direct sum of two copies of the Lie algebra so(3) of SO(3). This enables one to decompose the tangent bundle of the manifold into a direct sum of two oriented 3-plane bundles. The curvature of the Levi-Civita connection then splits with respect to this decomposition, the decomposition having entries involving the scalar curvature, the traceless Ricci tensor, and the self-dual and anti-self dual Weyl curvature tensors. The question of the existence of metrics on the manifold for which the anti-self dual part vanishes is the subject of the book, with particular attention paid to complex vector bundles over the manifold. The anti-self dual equations are consequently a set of algebraic equations for the curvature, which are equivalent, over an open set in the manifold, to a first-order differential equation involving a 1-form over this open set and taking values in the Lie algebra of complex 2-space.The main strategy the author employs for studying these equations is to showthat they linearize to Fredholm equations. Thus a kind of generalization of the Fredholm property holds here in the context of (infinite-dimensional) vector bundles. A section of an infinite-dimensional vector bundle which linearizes to a Fredholm operator acts essentially like a section of a finite dimensional bundle over a finite dimensional manifold.

The book could also be used to motivate a study of the connection between the Donaldson and Seiberg-Witten invariants of smooth four-manifolds. That there is such a connection was recently conjectured and some promising work in proving this conjecture has appeared lately. There has also been recent interest in examining the anti-self dual equations on noncommutative four-dimensional Euclidean space, because of its connection with string theory. ... Read more

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This monograph discusses important results in the fields of differential geometry and topology. It sets the framework for development in these areas and should be a useful reference tool for both students and researchers in these fields. ... Read more

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Four papers by C.H. Taubes (Harvard University) comprising the complete proof of his remarkable result relating the Seiberg-Witten and Gromov invariants of symplectic four manifolds.2010 paperback re-issue. ... Read more

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Les achats comprennent une adhésion à l'essai gratuite au club de livres de l'éditeur, dans lequel vous pouvez choisir parmi plus d'un million d'ouvrages, sans frais. Le livre consiste d'articles Wikipedia sur : Saul Bellow, Lester Bowles Pearson, Robert Mundell, Rudolph Marcus, Henry Taube, David Hunter Hubel, Frederick Banting, William Vickrey, Willard Boyle, John Charles Polanyi, Bertram Brockhouse, Michael Smith, Richard E. Taylor, John James Richard Macleod, Charles Brenton Huggins, William Francis Giauque, Myron Scholes, Gerhard Herzberg, Sidney Altman. Non illustré. Mises à jour gratuites en ligne. Extrait : Saul Bellow (né le 10 juillet 1915 à Lachine, Québec - mort le 5 avril 2005 à Brookline, Massachusetts, États-Unis) est un écrivain américain contemporain d'origine juive-russe. Il reçut le Prix Nobel de littérature en 1976. Né à Lachine (Québec) - maintenant Montréal - en 1915, fils d'immigrés juifs-russes, élevé à l'école de la rue mais universitaire de carrière (notamment à Chicago), Saul Bellow a obtenu trois fois le National Book Award, pour Les aventures d'Augie March (1953), Herzog (1964) et La planète de M. Sammler (1969). Consacré « meilleur écrivain américain de sa génération », devant Norman Mailer, le Nobel le glorifie en 1976. Cet artiste qui mêle l'argot à la métaphysique juive, cinq fois divorcé, vivait entre le Vermont et Boston, remarié à une ex-étudiante de trente ans sa cadette, lorsqu'il décède en 2005. Ses parents ont émigré de Russie vers le Canada en 1913. Bellow a été élevé jusqu'à l'âge de 9 ans dans un quartier pauvre de Montréal, habité par des Russes, des Polonais, des Ukrainiens, des Grecs et des Italiens. Après la mort de son père (qui faisait le bootlegger - soit la distillation et le trafic d'alcool clandestin) la famille s'en alla en 1924 à Chicago. Bien que Bellow ne soit pas considéré comme un écrivain à l'écriture autobiographique, ses racines canadiennes jouent un rôle dans son p...http://booksllc.net/?l=fr ... Read more

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Chapters: Robert Latimer, Peter Vasilevich Verigin, Lois Hole, Seager Wheeler, Connie Fogal, C. Donald Bateman, Henry Taube, E. K. Turner, Cal Nichols, James Weisgerber, Harlo Jones, Frank Cole, Albert Wesley Johnson, Russell Honey, Ron Cochran, Rod Zimmer, Arthur B. Metzner, Douglas Barber, John James Deutsch, Robert Steadward, Boyd Wettlaufer, Harry Archibald, Gerry Mcalpine, Arnold Spohr, Norine Burgess, Maurice Moreau, Amanda Putz, Gerald Bouey, Jim Lang, Darren Dutchyshen, William Doyle, Bill Small, Floyd Glass. Source: Wikipedia. Pages: 104. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Robert William "Bob" Latimer (born March 13, 1953), a Canadian canola and wheat farmer, was convicted of second-degree murder in the death of his daughter Tracy (November 23, 1980 October 24, 1993). This case sparked a national controversy on the definition and ethics of euthanasia as well as the rights of people with disabilities, and two Supreme Court decisions, R. v. Latimer (1997), on section 10 of the Canadian Charter of Rights and Freedoms, and later R. v. Latimer (2001), on cruel and unusual punishments under section 12 of the Charter. Latimer was released on day parole in March 2008 and will be eligible to apply for full parole in December 2010. Before his imprisonment, Bob Latimer lived near Wilkie, Saskatchewan, on a 1,280 acres (520 ha) wheat and canola farm with his wife, Laura, and their four children. Tracy Latimer was born November 23, 1980. An interruption in Tracy's supply of oxygen during the birth caused cerebral palsy, leading to severe mental and physical disabilities including seizures that were controlled with seizure medication. She had little or no voluntary control of her muscles, wore diapers, and could not walk or talk. Her doctors described the care given by her family a...More: http://booksllc.net/?id=649026 ... Read more

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Les achats comprennent une adhésion à l'essai gratuite au club de livres de l'éditeur, dans lequel vous pouvez choisir parmi plus d'un million d'ouvrages, sans frais. Le livre consiste d'articles Wikipedia sur : Linus Pauling, Robert Mulliken, Peter Debye, Henry Taube, Frank Albert Cotton, Harold Clayton Urey, George Whitesides, Paul J. Flory, Glenn Theodore Seaborg, Thomas Midgley Jr., Harry B. Gray, Louis Plack Hammett, James Bryant Conant, Melvin Calvin, George A. Olah, Henry Eyring, Fred Basolo, Herbert C. Brown, Derek Harold Richard Barton, Edgar Fahs Smith, Robert Robinson, Elias James Corey, Ira Remsen, Roald Hoffmann, George S. Hammond, Carl Djerassi. Non illustré. Mises à jour gratuites en ligne. Extrait : Linus Carl Pauling, né le 28 février 1901 et mort le 19 août 1994, était un chimiste et physicien américain. Il fut l'un des premiers chimistes quantiques, et reçut le prix Nobel de chimie en 1954 pour ses travaux décrivant la nature de la liaison chimique. Il publie en 1939 un ouvrage majeur La Nature de la liaison chimique (The Nature of the Chemical Bond) dans lequel il développe le concept d'hybridation des orbitales atomiques. Ses travaux sur les substituts de plasma sanguin (avec Harvey Itano) durant la Seconde Guerre mondiale, ainsi que ses recherches concernant l'anémie falciforme (ou drépanocytose qu'il qualifie du terme révolutionnaire de « maladie moléculaire ») ont grandement influencé la recherche en biologie pour la seconde moitié du siècle. Il découvrira notamment la structure de l'hélice alpha (motif d'enroulement secondaire des protéines) et manquera de peu la découverte de la structure en double hélice de l'acide désoxyribonucléique (ADN). Il proposera en effet une structure en hélice triple, structure dont l'amélioration d'après l'étude de l'ADN par radiocristallographie aurait vraisemblablement pu l'amener à l'élaboration du modèle en double hélice proposé par James Dewey Watson et Francis Crick ...http://booksllc.net/?l=fr ... Read more

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Les achats comprennent une adhésion à l'essai gratuite au club de livres de l'éditeur, dans lequel vous pouvez choisir parmi plus d'un million d'ouvrages, sans frais. Le livre consiste d'articles Wikipedia sur : Dmitri Mendeleïev, Linus Pauling, Henri Moissan, Paul Sabatier, Henry Taube, Richard R. Schrock, Frank Albert Cotton, Alfred Werner, Robert H. Crabtree, Geoffrey Wilkinson, Edmond Frémy, Ronald Sydney Nyholm, Fred Basolo, Herbert C. Brown, Ernst Otto Fischer, Ronald Gillespie, Neil Bartlett, William Nunn Lipscomb. Non illustré. Mises à jour gratuites en ligne. Extrait : Linus Carl Pauling, né le 28 février 1901 et mort le 19 août 1994, était un chimiste et physicien américain. Il fut l'un des premiers chimistes quantiques, et reçut le prix Nobel de chimie en 1954 pour ses travaux décrivant la nature de la liaison chimique. Il publie en 1939 un ouvrage majeur La Nature de la liaison chimique (The Nature of the Chemical Bond) dans lequel il développe le concept d'hybridation des orbitales atomiques. Ses travaux sur les substituts de plasma sanguin (avec Harvey Itano) durant la Seconde Guerre mondiale, ainsi que ses recherches concernant l'anémie falciforme (ou drépanocytose qu'il qualifie du terme révolutionnaire de « maladie moléculaire ») ont grandement influencé la recherche en biologie pour la seconde moitié du siècle. Il découvrira notamment la structure de l'hélice alpha (motif d'enroulement secondaire des protéines) et manquera de peu la découverte de la structure en double hélice de l'acide désoxyribonucléique (ADN). Il proposera en effet une structure en hélice triple, structure dont l'amélioration d'après l'étude de l'ADN par radiocristallographie aurait vraisemblablement pu l'amener à l'élaboration du modèle en double hélice proposé par James Dewey Watson et Francis Crick en 1953. Il est l'un des fondateurs de la médecine orthomoléculaire et a popularisé l'utilisation de la vitamine C. Il reçut aussi le prix N...http://booksllc.net/?l=fr ... Read more

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Les achats comprennent une adhésion à l'essai gratuite au club de livres de l'éditeur, dans lequel vous pouvez choisir parmi plus d'un million d'ouvrages, sans frais. Le livre consiste d'articles Wikipedia sur : Henry Taube, John Charles Polanyi, Michael Smith, Ronald Gillespie, William Fyfe, Gerhard Herzberg, Joseph Schwarcz, André Bandrauk, Edgar William R. Steacie, Léo Marion, Howard Alper, James Watson Bain, Jane Barry, Raymond Lemieux, Richard Bader. Non illustré. Mises à jour gratuites en ligne. Extrait : Henry Taube (30 novembre 1915 à Neudorf, Saskatchewan, Canada - 16 novembre 2005 à Palo Alto, Californie) était un chimiste canadien naturalisé américain. Il est récipiendaire du prix Nobel de chimie de 1983. Fils d'agriculteurs d'origine allemande qui ont émigré d'Ukraine vers le Canada, Henri Taube suit des études universitaires à l'université de la Saskatchewan où il obtient un B.S. (1935) et un M.Sc. (1937). Il part ensuite pour l'université de Californie et obtient un Ph.D. sous la direction de William Bray (1940). Il poursuit ensuite une carrière universitaire, et devient professeur de chimie dans les universités de Cornell (1941-1946), Chicago (1946-1962) et Stanford (1962-2001), où il devient professeur émérite en 1986. Il sera aussi consultant au département de l'Énergie des États-Unis du laboratoire national de Los Alamos et chez Catalytica Associates Inc. (Mountain View, Californie). Henri Taube est naturalisé citoyen américain en 1942. Durant sa carrière, Henri Taube s'intéresse aux réactions d'oxydo-réduction, dans lesquelles des électrons sont perdus ou gagnés au cours d'une réaction chimique. Ses travaux révolutionnaires s'articulent autour de l'étude des transferts électroniques dans le domaine de la chimie de coordination, qui est l'étude de métaux de transition entourés par d'autres molécules ou ions. Il utilise notamment des isotopes et des études photochimiques pour sonder ces réactions. Ces travaux ...http://booksllc.net/?l=fr ... Read more

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This book focuses on the differential equations and related subjects that are commonly used today by working life scientists. It emphasizes both the mathematics and how the mathematics is employed in order to introduce some potentially useful tools and modes of thought to future experimental biologists.Chapter topics include phase plane analysis, vectors, linear and non-linear systems, matrix notation, advection, diffusion equations, separation of variables, traveling waves, and periodic solutions.For individuals interested in biology and the life sciences, and aware of how they will play a major role in our society in the coming century. y. ... Read more

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Stories of Jewish youth who were victims of the Holocaust. ... Read more

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This digital document is an article from Canadian Chemical News, published by Thomson Gale on February 1, 2006. The length of the article is 655 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

Citation Details
Title: In memoriam.(Henry Taube, J. E. Guillet)(Obituary)
Publication: Canadian Chemical News (Magazine/Journal)
Date: February 1, 2006
Publisher: Thomson Gale
Volume: 58Issue: 2Page: 4(1)

Article Type: Obituary

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This 204 page book contains lectures delivered and abstracts of papers submitted to the 1959 conference.Contents includes:*New Aspects of Some Organometallic Complex Compounds. By Ziegler*The Stability of Metal Complexes. BY Irving*Metal Carbonyls & Related Compounds as Catalytic Intermediates in Organic Syntheses. By Sternberg and Wender*Mechanisms of Complex Ion Reactions: Recent Advances. By Taube*Co-ordination Compounds of Unsaturated Hydrocarbons with metals. By Fischer*Metal-Ligand Bonds. By Orgel*Complex Acetylides of Transition Metals. By Nast*Abstracts of Papers*Index of Authors*Index of Subjects ... Read more

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The book contains a complete proof of the remarkableresult relating the Seiberg-Witten and Gromov invariants of symplecticfour manifolds.The first chapter proves that pseudo-holomorphiccurves can be sonstruction from solutions to the Seiberg-Wittenequations.The second chapter describes how the Gromov invariant forcompact symplectic 4-manifolds assigns an integer to each dimension2-cohomology class (or roughly speaking, counts with suitable weights,compact, pseudo-holomorphic submanifolds whose fundamental class isPoincare dual to the cohomology class in question.The third chaptercontinues the proof of the equivalence of Gromov invariants and theSeiberg-Witten invariants.In this chapter, a construction whichassociates solutions of the one-parameter family of Weiber-Wittenequations to certain symplectic submanifolds in X (Pseudo-holomorphicones.)The final chapter shows that counting for the two invariantsyeilds the same answer. ... Read more

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Andreas Floer died on May 15, 1991 an untimely and tragic death. His visions and far-reaching contributions have significantly influenced the developments of mathematics. His main interests centered on the fields of dynamical systems, symplectic geometry, Yang-Mills theory and low dimensional topology. Motivated by the global existence problem of periodic solutions for Hamiltonian systems and starting from ideas of Conley, Gromov and Witten, he developed his Floer homology, providing new, powerful methods which can be applied to problems inaccessible only a few years ago. This volume opens with a short biography and three hitherto unpublished papers of Andreas Floer. It then presents a collection of invited contributions, and survey articles as well as research papers on his fields of interest, bearing testimony of the high esteem and appreciation this brilliant mathematician enjoyed among his colleagues.Authors include: A. Floer, V.I. Arnold, M. Atiyah, M. Audin, D.M. Austin, S.M. Bates, P.J. Braam, M. Chaperon, R.L. Cohen, G. Dell' Antonio, S.K. Donaldson,B. D'Onofrio, I. Ekeland, Y. Eliashberg, K.D. Ernst, R. Finthushel, A.B. Givental,H. Hofer, J.D.S. Jones, I. McAllister, D. McDuff, Y.-G. Oh, L. Polterovich, D.A. Salamon, G.B. Segal, R. Stern, C.H. Taubes, C. Viterbo, A. Weinstein, E. Witten,E. Zehnder ... Read more