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Author | : Lizhen Ji |
Publisher | : American Mathematical Soc. |
Total Pages | : 282 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 0821848666 |
Download Arithmetic Groups and Their Generalizations Book in PDF, ePub and Kindle
In one guise or another, many mathematicians are familiar with certain arithmetic groups, such as $\mathbf{Z}$ or $\textrm{SL}(n, \mathbf{Z})$. Yet, many applications of arithmetic groups and many connections to other subjects within mathematics are less well known. Indeed, arithmetic groups admit many natural and important generalizations. The purpose of this expository book is to explain, through some brief and informal comments and extensive references, what arithmetic groups and their generalizations are, why they are important to study, and how they can be understood and applied to many fields, such as analysis, geometry, topology, number theory, representation theory, and algebraic geometry. It is hoped that such an overview will shed a light on the important role played by arithmetic groups in modern mathematics. Titles in this series are co-published with International Press, Cambridge, MA.Table of Contents: Introduction; General comments on references; Examples of basic arithmetic groups; General arithmetic subgroups and locally symmetric spaces; Discrete subgroups of Lie groups and arithmeticity of lattices in Lie groups; Different completions of $\mathbb{Q}$ and $S$-arithmetic groups over number fields; Global fields and $S$-arithmetic groups over function fields; Finiteness properties of arithmetic and $S$-arithmetic groups; Symmetric spaces, Bruhat-Tits buildings and their arithmetic quotients; Compactifications of locally symmetric spaces; Rigidity of locally symmetric spaces; Automorphic forms and automorphic representations for general arithmetic groups; Cohomology of arithmetic groups; $K$-groups of rings of integers and $K$-groups of group rings; Locally homogeneous manifolds and period domains; Non-cofinite discrete groups, geometrically finite groups; Large scale geometry of discrete groups; Tree lattices; Hyperbolic groups; Mapping class groups and outer automorphism groups of free groups; Outer automorphism group of free groups and the outer spaces; References; Index. Review from Mathematical Reviews: ...the author deserves credit for having done the tremendous job of encompassing every aspect of arithmetic groups visible in today's mathematics in a systematic manner; the book should be an important guide for some time to come.(AMSIP/43.
Author | : |
Publisher | : |
Total Pages | : 415 |
Release | : 1994 |
Genre | : Linear algebraic groups |
ISBN | : |
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Author | : Armand Borel |
Publisher | : American Mathematical Soc. |
Total Pages | : 118 |
Release | : 2019-11-07 |
Genre | : Education |
ISBN | : 1470452316 |
Download Introduction to Arithmetic Groups Book in PDF, ePub and Kindle
Fifty years after it made the transition from mimeographed lecture notes to a published book, Armand Borel's Introduction aux groupes arithmétiques continues to be very important for the theory of arithmetic groups. In particular, Chapter III of the book remains the standard reference for fundamental results on reduction theory, which is crucial in the study of discrete subgroups of Lie groups and the corresponding homogeneous spaces. The review of the original French version in Mathematical Reviews observes that “the style is concise and the proofs (in later sections) are often demanding of the reader.” To make the translation more approachable, numerous footnotes provide helpful comments.
Author | : William Joseph Haboush |
Publisher | : |
Total Pages | : 383 |
Release | : 1994 |
Genre | : Linear algebraic groups |
ISBN | : 9780821814970 |
Download Algebraic Groups and Their Generalizations Book in PDF, ePub and Kindle
Author | : V. E. Voskresenskii |
Publisher | : American Mathematical Soc. |
Total Pages | : 234 |
Release | : 2011-10-06 |
Genre | : Mathematics |
ISBN | : 0821872885 |
Download Algebraic Groups and Their Birational Invariants Book in PDF, ePub and Kindle
Since the late 1960s, methods of birational geometry have been used successfully in the theory of linear algebraic groups, especially in arithmetic problems. This book--which can be viewed as a significant revision of the author's book, Algebraic Tori (Nauka, Moscow, 1977)--studies birational properties of linear algebraic groups focusing on arithmetic applications. The main topics are forms and Galois cohomology, the Picard group and the Brauer group, birational geometry of algebraic tori, arithmetic of algebraic groups, Tamagawa numbers, $R$-equivalence, projective toric varieties, invariants of finite transformation groups, and index-formulas. Results and applications are recent. There is an extensive bibliography with additional comments that can serve as a guide for further reading.
Author | : William Joseph Haboush |
Publisher | : |
Total Pages | : 0 |
Release | : 1994 |
Genre | : Linear algebraic groups |
ISBN | : |
Download Algebraic Groups and Their Generalizations Book in PDF, ePub and Kindle
Author | : Athanase Papadopoulos |
Publisher | : European Mathematical Society |
Total Pages | : 876 |
Release | : 2007 |
Genre | : Teichm uller spaces |
ISBN | : 9783037191033 |
Download Handbook of Teichmüller Theory Book in PDF, ePub and Kindle
The subject of this handbook is Teichmuller theory in a wide sense, namely the theory of geometric structures on surfaces and their moduli spaces. This includes the study of vector bundles on these moduli spaces, the study of mapping class groups, the relation with $3$-manifolds, the relation with symmetric spaces and arithmetic groups, the representation theory of fundamental groups, and applications to physics. Thus the handbook is a place where several fields of mathematics interact: Riemann surfaces, hyperbolic geometry, partial differential equations, several complex variables, algebraic geometry, algebraic topology, combinatorial topology, low-dimensional topology, theoretical physics, and others. This confluence of ideas toward a unique subject is a manifestation of the unity and harmony of mathematics. This volume contains surveys on the fundamental theory as well as surveys on applications to and relations with the fields mentioned above. It is written by leading experts in these fields. Some of the surveys contain classical material, while others present the latest developments of the theory as well as open problems. This volume is divided into the following four sections: The metric and the analytic theory The group theory The algebraic topology of mapping class groups and moduli spaces Teichmuller theory and mathematical physics This handbook is addressed to graduate students and researchers in all the fields mentioned.
Author | : William Joseph Haboush |
Publisher | : |
Total Pages | : |
Release | : 1994 |
Genre | : Linear algebraic groups |
ISBN | : |
Download Algebraic Groups and Their Generalizations Book in PDF, ePub and Kindle
Author | : Stefan Witzel |
Publisher | : Springer |
Total Pages | : 128 |
Release | : 2014-07-16 |
Genre | : Mathematics |
ISBN | : 3319064770 |
Download Finiteness Properties of Arithmetic Groups Acting on Twin Buildings Book in PDF, ePub and Kindle
Providing an accessible approach to a special case of the Rank Theorem, the present text considers the exact finiteness properties of S-arithmetic subgroups of split reductive groups in positive characteristic when S contains only two places. While the proof of the general Rank Theorem uses an involved reduction theory due to Harder, by imposing the restrictions that the group is split and that S has only two places, one can instead make use of the theory of twin buildings.
Author | : Armand Borel |
Publisher | : |
Total Pages | : 0 |
Release | : 2020 |
Genre | : Arithmetic groups |
ISBN | : 9787040533750 |
Download Arithmetic Groups and Reduction Theory Book in PDF, ePub and Kindle
Presents papers and lecture notes from four great contributors of the reduction theory: Armond Borel, Roger Godement, Carl Ludwig Siegel and Andre Weil. They reflect their deep knowledge of the subject and their perspectives.