Geometry.Net - Pure_And_Applied_Math: Algebraic Topology

Algebraic Topology And Algebraic Geometry Research Group, Univ. Of Calgary
algebraic topology and Algebraic Geometry research group. Research category.Researcher. algebraic topology. Peter Zvengrowski. 55R25, 55N15, 55M30.
http://www.math.ucalgary.ca/~cunning/topgeo.html

Extractions: Research at the Department of Mathematics Research category Researcher AMS subject classification Research topics Algebraic Geometry Len Bos Real analytic and semianalytic sets; Algebraic Geometry Alex Brudnyi Homotopy theory; fundamental groups Algebraic Geometry Clifton Cunningham Rigid analytic geometry General topology Kalathoor Varadarajan $C$- and $C^*$-embedding; Remainders; Extremally disconnected spaces, $F$-spaces, etc.; Pathological spaces General topology Claude Laflamme Remainders; Continua and generalizations Algebraic topology Peter Zvengrowski Algebraic topology Kalathoor Varadarajan Bordism and cobordism theories, formal group laws Algebraic topology Jonathan Schaer Degree, winding number; Finite groups of transformations (including Smith theory) Manifolds and cell complexes Igov Nikolaev Geometric structures on low-dimensional manifolds; Topology of $E^2$, $2$-manifolds Manifolds and cell complexes Larry Bates Compact Lie groups of differentiable transformations; Noncompact Lie groups of transformations Manifolds and cell complexes Peter Zvengrowski Vector fields, frame fields; Topology of general $3$-manifolds ; Specialized structures on manifolds (spin manifolds, framed manifolds, etc.); Homology and cohomology of homogeneous spaces of Lie groups
The Kenzo Program.
A computer program for computational algebraic topology.
http://www-fourier.ujf-grenoble.fr/~sergerar/Kenzo/

Extractions: The Kenzo program is the last version (16000 Lisp lines, July 1998) of the CAT (= Constructive Algebraic Topology) computer program. Kenzo is also the name of my cat . The Kenzo program is a joint work with Xavier Dousson. The previous version EAT (May 1990) was a joint work with Julio Rubio. The Kenzo program is significantly more powerful than EAT, from several points of view. On one hand, for the computations which could be done with the EAT program, the computing times are divided by a factor generally between 10 and 100. The reasons are multiple and it is not obvious to decide what the most important are. Some are strictly technical; for example the numerous multi-degeneracy operators are now coded with a unique integer, using an amusing binary trick: various tests show much progress has been obtained in this way. Other reasons are strictly mathematical; for example another choice for the Eilenberg-Zilber homotopy operator leads in the Kenzo program to Szczarba's universal twisting cochain; in the EAT program we used Shih's universal twisting cochain; experience shows that Szczarba's cochain is considerably more efficient than Shih's one. It is a major mathematical problem to understand
Unit Description: Algebraic Topology
for 2002/2003. algebraic topology (MATH 41200).Contents of this document Texts. Maunder algebraic topology. Syllabus. Undergraduate Unit
http://www.maths.bris.ac.uk/~madhg/unitinfo/current/l4_units/alg_top.htm

Extractions: Texts and Syllabus Unit number and title: MATH 41200 Algebraic topology Level: Credit point value: 20 credit points Year: First given in this form: 1997/8 (but a similar course was given some years ago) Lecturer/organiser: Dr. A. Lazarev Semester: Timetable: Monday 9.00, Wednesday 9.00, Friday 9.00 Prerequisites: Level 2 Analysis Level 3 Group Theory The aim of the unit is to give an introduction to algebraic topology with an emphasis on homotopy and simplicial complexes and a brief introduction to homology. We begin by discussing relevant topics in general topology. These include compactness, path-connected spaces, Hausdorff spaces, convex spaces and the compact-Hausdorff lemma. We define homotopy between continuous functions, contractibility, homotopic spaces. We calculate the fundamental group of the circle and use this to prove the Fundamental Theorem of Algebra. We introduce simplicial complexes in order to provide a more general method for calculating the fundamental group. In order to prove this method works we need the Simplicial Approximation Theorem. We introduce homology and again use the simplicial approximation theorem to show how to calculate this for simplicial complexes. In the section on homology, the geometric methods are in the main sketched whilst the algebraic results have rigorous proofs.
Algebraic Topology
algebraic topology MATH 8200. UGA, Spring 2003. The textbook is A Basic Course inalgebraic topology, by William S. Massey. It is available at the UGA bookstore.
http://www.math.uga.edu/~clint/2003/8200/topology.htm

Extractions: - or by appointment - Syllabus The textbook is A Basic Course in Algebraic Topology , by William S. Massey. It is available at the UGA bookstore. One goal of this course is to prepare Ph.D. candidates for the written qualifying exam in topology. We'll cover the first nine chapters of Massey's book: surfaces, the fundamental group, free products, van Kampen's theorem, covering spaces, homology groups, applications of homology, CW complexes. The background required for this course is point set topology (MATH 4200/6200, a formal course prerequisite) and basic group theory (as in MATH 4010/6010). Notes from class Clasification of surfaces with boundary
HMC Math 177a -- Algebraic Topology
Math 177a Special Topics algebraic topology Text Munkres, Elements of AlgebraicTopology. Doing the reading will be essential for success in this course.
http://www.math.hmc.edu/~su/math177a/

Extractions: Office Hours: WED 1-2:30pm. Course Content: This course is an introduction to algebraic and combinatorial topology, with an emphasis on simplicial and singular homology theory. A major theme in the course will be the connection between combinatorial and topological concepts. Topics will include simplicial complexes, simplicial and singular homology groups, exact sequences, chain maps, diagram chasing, Mayer-Vietoris sequences, Eilenberg-Steenrod axioms, Jordan curve theorem, and additional topics as time permits. This is standard first-year graduate material in pure mathematics. Text: Munkres, Elements of Algebraic Topology . Doing the reading will be essential for success in this course. Prerequisites: Analysis I (Math 131), Algebra I (Math 171), and Topology (Math 147, or topology summer readings), or the permission of the instructor. I will try to set up a few extra sessions to meet with those who did the summer readings. A note about the course: Expect this course to be challenging, but also quite rewarding, as you see the interplay between algebra, topology, combinatorics, and analysis. I will run this course more like a graduate course. As such, I will expect a certain level of mathematical maturity. This means that sometimes I will not prove simple statements in class; you may have to work out some details for yourself or by doing the reading. My focus will be on proving the larger theorems and providing perspective on the material.
GARY PRESS PUBLISHING, The Rear Annex, Suite 514, 9728 Third Avenue, Brooklyn, N
. algebraic topology. Concepts in algebraic topology. logo The Continuing Adventures of 'V' . algebraic topology. Avian Publications. OurCorporate
http://home.att.net/~gary_press/wsb/html/view.cgi-category.html-TopCat-Algebraic
Algebraic Topology And Groups
Amir H. Assadi. Publications Related to Applications of algebraic topology,Algebraic Ktheory, L-theory and Surgery in Finite Transformation Groups.
http://www.cms.wisc.edu/~cvg/Pubs/transgs.html

Extractions: Amir H. Assadi Publications Related to Applications of Algebraic Topology, Algebraic K-theory, L-theory and Surgery in Finite Transformation Groups Some Examples of Finite Group Actions, Proc. of Waterloo Conference, 1978, Lecture Notes in Math. Springer-Verlag, No. 741 (1979) 206-220. Finite Group Actions on Simply- connected Manifolds and CW Complexes. Memoirs AMS No. 257, January 1982, pp. 116 + x. (Expanded version of Ph.D. Thesis 1979 Princeton University). Extensions of Finite Group Actions from Submanifolds of a Disk, Proceedings of London Topology Conference Ontario, Canada 1981, under the title "Current Trends in Algebraic Topology" American Mathematical Society (1982), 45-66. (A research announcement can be found in "Aarhus Topology Seminars" Editor, I. Madsen 1982). Concordance of Finite Group Actions on Spheres. Contem. Math. AMS Vol 35, (1985), 299-310. On the Existence and Classification of Extensions of Actions of Finite Groups on Submanifolds of Disks and Spheres (with W. Browder). Transactions AMS (291), 487-502 (1985). Homotopy Actions and Cohomology of Finite Groups. Proceedings of Transformation Groups, Poznan, Poland, July 1985, Springer-Verlag LNM 1217 (1986) 26-57.
Course 421 - Algebraic Topology
Course 421 algebraic topology. Lecture Notes for the Academic Year2002-3. The following lecture notes for the academic year 2002
http://www.maths.tcd.ie/~dwilkins/Courses/421/

Extractions: The following lecture notes for the academic year 2002-3 are currently available:- The following problems sets for the academic year 2002-3 are currently available:- The lecture notes for course 421 ( Algebraic topology ), taught at Trinity College, Dublin, in the academic year 1998-1999, are available also here. (Note that the syllabus for the course as taught that year differs from the current syllabus.) The course consisted of four parts:- dwilkins@maths.tcd.ie Dr. David R. Wilkins
Algebraic Topology At Fukuoka
algebraic topology at Fukuoka. Click here for Japanese version.
http://www.sm.fukuoka-u.ac.jp/~topology/index-e.html
Rubriek: 31.61 Algebraic Topology
DutchESS, Dutch Electronic Subject Service, Rubriek 31.61 algebraic topology.
http://www.kb.nl/dutchess/31/61/
Algebraic Topology
algebraic topology.Benjamin (1967); Rotman, JJ An introduction to algebraic topology.
http://www.mathematik.uni-kl.de/~lossen/LECTURES/Alg_Topology.html
Algebraic Topology Innovations And Patents
algebraic topology Innovations and Patents © 2002, XQ23.COM ResearchBanding analysis Biochemical Indicators Biological Dosimetry
http://databank.oxydex.com/prospecting_for_knowledge/Algebraic_Topology.html
Browder, W., Ed.: Algebraic Topology And Algebraic K-Theory: Proceedings Of A Sy
of the book algebraic topology and Algebraic KTheoryProceedings of a Symposium in Honor of John C. Moore. (AM-113
http://pup.princeton.edu/titles/2548.html

Extractions: Shopping Cart: For customers in the U.S., Canada, Latin America, Asia, and Australia Paper: $55.00 ISBN: 0-691-08426-2 For customers in England, Europe, Africa, the Middle East, and India Prices subject to change without notice File created: 12/6/02 Questions and comments to: webmaster@pupress.princeton.edu
MATH 7520 Algebraic Topology
MATH 7520 algebraic topology. Fall 2002. Course Information. CourseMATH 7520 algebraic topology. Time and Place Tuesday
http://www.math.lsu.edu/~cohen/courses/FALL02/M7520/M7520.html

Extractions: Some other sources for material covered in this course are listed below. A fundamental problem in topology is that of determining, for two spaces, whether or not they are topologically equivalent. The basic idea of algebraic topology is to associate algebraic objects (groups, rings, etc.) to a topological space in such a way that topologically equivalent spaces get assigned isomorphic objects. The fundamental group introduced in MATH 7512 is one example. Such algebraic objects are invariants of the space, and provide a means for distinguishing between topological spaces. Two spaces with inequivalent invariants cannot be topologically equivalent. The focus of this course will be on homology theory (which complements the study of algebraic topology begun in MATH 7512). To a topological space, we will associate a sequence of abelian groups, called the homology groups. These homology groups are often more accessible than the fundamental group, so sometimes provide an easier means for distinguishing between topological spaces. We will concretely study simplicial and singular homology, the homology of CW-complexes, and related topic such as homology with coefficients, Mayer-Vietoris sequences, degrees of maps, and Euler characteristics. Geometric examples, including surfaces, projective spaces, lens spaces, etc., will be used to illustrate the techniques. We will also discuss a number of applications, including Brouwer and Lefschetz Fixed Point Theorems, and the Jordan Curve Theorem.
SC_39 Algebraic Topology
algebraic topology. Suzhou University, Suzhou, Aug. 30 Sep. 3,2002. Topics This conference will focus on the main problem and
http://www.icm2002.org.cn/satellite/satel_39.htm

Extractions: Welcome What's New General Information Organization ... FAQ Algebraic Topology Suzhou University, Suzhou, Aug. 30 - Sep. 3, 2002 Topics: This conference will focus on the main problem and the important progress of algebraic topology and differential topology, e.g., spectral sequence, cobordism, localization, embedding,immersion, etc.
CONTEMPORARY TRENDS IN ALGEBRAIC GEOMETRY AND ALGEBRAIC TOPOLOGY
5 CONTEMPORARY TRENDS IN ALGEBRAIC GEOMETRY AND algebraic topology edited by ShiingShenChern, Lei Fu (Nankai Institute of Mathematics, PR China) Richard
http://www.wspc.com/books/mathematics/4966.html

Extractions: The Chern Visiting Professorship, begun in 1996, honors the Berkeley professor emeritus widely regarded as the greatest geometer of his generation. "Chern's belief in young people and his encouragement of them had a lot to do with the spectacular growth of geometry in the second half of this century" mathematician Blaine Lawson has said. "It is not easy to find a geometer who was not for some period of time either a student or a post-doctoral fellow in the orbit of Chern. (http://math.berkeley.edu/)
Algebraic Topology Course
algebraic topology Course, 2002/2003, Instructor Boris Botvinnik. The class meetson MWF at 900 am Deady 210. Problem Session Friday, 300 pm Deady 210.
http://www.uoregon.edu/~botvinn/634.html

Extractions: NOTES FOR THE COURSE: Section 1. First set of the most important topological spaces p. 1-7 Section 2. Constructions p. 8-12 Section 3. Homotopy and homotopy equivalence p. 13-18 Section 4. CW-complexes p. 19-26 Section 5. CW-complexes and homotopy p. 27-35 Section 6. Fundamental group p. 36-44 Section 7. Covering spaces p. 45-52 Section 8. Higher homotopy groups p. 53-58 Section 9. Fiber bundles p. 58-67 Section 10. Suspension Theorem and Whitehead product p. 68-78 Section 11. Homotopy groups of CW-complexes p. 79-91 Section 12. Homology groups: basic constructions p. 92-104 Section 13. Homology groups of CW-complexes p. 104-115 Section 14. Homology and homotopy groups p. 115-121 Section 15. Homology with coefficients and cohomology groups p. 121-136 Section 16. Some applications p. 136-142 Section 17. Cup product in cohomology p. 142-151 Boris Botvinnik
M.I.T. Algebraic Topology Seminar
MIT algebraic topology Seminar. Monday, 430pm530pm Room 2- 131. Thispage has move to http//www-math.mit.edu/~sharon/alg_top_sem.html.
http://www-math.mit.edu/~jg/alg_top_sem.html
Conferences And Activities - Barcelona Algebraic Topology Group
1998 Barcelona Conference on algebraic topology. CRM Advanced Course on ClassifyingSpaces and Cohomology of Groups (1998). algebraic topology Semester (1998).
http://manwe.mat.uab.es/topalg/page_Activities_.html

Extractions: Conferences and Activities Barcelona 2001 Euro PhD Topology Conference Bellaterra 3-7 July, 2001. First Euro-Mediterranean Topology Meeting , a satellite conference of the Third European Congress of Mathematics 1998 Barcelona Conference on Algebraic Topology CRM Advanced Course on Classifying Spaces and Cohomology of Groups Algebraic Topology Semester (1998) The Little Barcelona Topology Workshop (1996) CRM Advanced Course on Localization and Periodicity (1996) CRM Advanced Course on Elliptic Cohomology (1995) 1994 Barcelona Conference on Algebraic Topology Algebraic Topology Semester (1994) 1990 Barcelona Conference on Algebraic Topology Algebraic Topology Semester (1990) 1986 Barcelona Conference on Algebraic Topology 1982 Workshop on Algebraic Topology
1.3.2 Algebraic Topology -- Dr Lackenby -- 16 HT
1.3.2 algebraic topology Dr Lackenby 16 HT. MJ Greenberg and JR Harper, AlgebraicTopology A First Course, Benjamin/Cummings (1981), first two parts.
http://www.maths.ox.ac.uk/teaching/synopses/2002/sect-c-02/node14.html

Extractions: Subsections Prerequisites : a4 Topology (b3 and a3 an advantage). When one studies topological spaces one is often interested in properties of the space that are left unchanged under deformation, called homotopy. One such example is given by the deformation theorem for contour integrals of a holomorphic function. The main idea in algebraic topology is to associate algebraic objects such as groups and rings to a space, which reflect its geometry up to these deformations. This allows algebraic topologists to prove statements such as ``one cannot comb a ball". While problems like this have been important for the development of the subject and illustrate its power, the ideas and techniques of homological algebra have by now entered into nearly every branch of mathematics. The algebraic invariant underlying the deformation theorem is the fundamental group, and this will be studied first. The second part of the course will introduce homology groups which will catch higher dimensional properties of the space. Tools like the Mayer-Vietoris sequence will help to compute the homology groups of a large number of spaces. 1.3.2.2 Synopsis

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