__Editorial Review__**Product Description** Discrete subgroups have played a central role throughout the development of numerous mathematical disciplines. Discontinuous group actions and the study of fundamental regions are of utmost importance to modern geometry. Flows and dynamical systems on homogeneous spaces have found a wide range of applications, and of course number theory without discrete groups is unthinkable. This book, written by a master of the subject, is primarily devoted to discrete subgroups of finite covolume in semi-simple Lie groups. Since the notion of "Lie group" is sufficiently general, the author not only proves results in the classical geometry setting, but also obtains theorems of an algebraic nature, e.g. classification results on abstract homomorphisms of semi-simple algebraic groups over global fields. The treatise of course contains a presentation of the author's fundamental rigidity and arithmeticity theorems. The work in this monograph requires the language and basic results from fields such as algebraic groups, ergodic theory, the theory of unitary representatons, and the theory of amenable groups. The author develops the necessary material from these subjects; so that, while the book is of obvious importance for researchers working in related areas, it is essentially self-contained and therefore is also of great interest for advanced students. ... Read more
__Customer Reviews (2)__
**The Perfect Supplement to RJ ZIMMER!**
As I read this masterpiece of 20th century mathematics, I couldn't help thinking of its relation to the book that defines modern group theory, RJ Zimmer's Ergodic Theory and Semisimple Groups.Coincidence?I think not.Robert Zimmer's book is simply the best there is, and Margoulis' brilliant work is an excellent supplement to that standard mathematical text.As the great Swiss mathematician Armand Borel once said, "Margoulis' masterpiece, while inferior to some of my own work, is an excellent supplement to Zimmer's classic.Zimmer's book is the standard to which all mathematicians should aspire (along with myself, bien sur).Other than my own work, Margoulis' comes as close as possible to reaching that standard."
**The Perfect Supplement to RJ ZIMMER!**
As I read this masterpiece of 20th century mathematics, I couldn't help thinking of its relation to the book that defines modern group theory, RJ Zimmer's Ergodic Theory and Semisimple Groups. Coincidence? I think not. Robert Zimmer's book is simply the best there is, and Margoulis' brilliant work is an excellent supplement to that standard mathematical text. As the great Swiss mathematician Armand Borel once said, "Margoulis' masterpiece, while inferior to some of my own work, is an excellent supplement to Zimmer's classic. Zimmer's book is the standard to which all mathematicians should aspire (along with myself, bien sur). Other than my own work, Margoulis' comes as close as possible to reaching that standard."
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