Kazhdan's Property (T) PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Kazhdan's Property (T) PDF full book. Access full book title Kazhdan's Property (T) by Bekka M Bachir La Harpe Pierre de Valette Alain. Download full books in PDF and EPUB format.
Author: Bekka M Bachir La Harpe Pierre de Valette Alain
Publisher:
ISBN: 9780511395116
Category : Mathematics
Languages : en
Pages : 488
Get Book Here
Book Description
A comprehensive introduction to the role of Property (T), with applications to an amazing number of fields within mathematics.
Author: Bekka M Bachir La Harpe Pierre de Valette Alain
Publisher:
ISBN: 9780511395116
Category : Mathematics
Languages : en
Pages : 488
Get Book Here
Book Description
A comprehensive introduction to the role of Property (T), with applications to an amazing number of fields within mathematics.
Author: Pierre-Alain Cherix
Publisher: Birkhäuser
ISBN: 3034882378
Category : Mathematics
Languages : en
Pages : 130
Get Book Here
Book Description
A locally compact group has the Haagerup property, or is a-T-menable in the sense of Gromov, if it admits a proper isometric action on some affine Hilbert space. As Gromov's pun is trying to indicate, this definition is designed as a strong negation to Kazhdan's property (T), characterized by the fact that every isometric action on some affine Hilbert space has a fixed point. This book is to covers various aspects of the Haagerup property. It gives several new examples.
Author: Armand Borel
Publisher: American Mathematical Soc.
ISBN: 1470452316
Category : Education
Languages : en
Pages : 133
Get Book Here
Book Description
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: Alex Lubotzky
Publisher: Springer Science & Business Media
ISBN: 3034603320
Category : Mathematics
Languages : en
Pages : 201
Get Book Here
Book Description
In the last ?fteen years two seemingly unrelated problems, one in computer science and the other in measure theory, were solved by amazingly similar techniques from representation theory and from analytic number theory. One problem is the - plicit construction of expanding graphs («expanders»). These are highly connected sparse graphs whose existence can be easily demonstrated but whose explicit c- struction turns out to be a dif?cult task. Since expanders serve as basic building blocks for various distributed networks, an explicit construction is highly des- able. The other problem is one posed by Ruziewicz about seventy years ago and studied by Banach [Ba]. It asks whether the Lebesgue measure is the only ?nitely additive measure of total measure one, de?ned on the Lebesgue subsets of the n-dimensional sphere and invariant under all rotations. The two problems seem, at ?rst glance, totally unrelated. It is therefore so- what surprising that both problems were solved using similar methods: initially, Kazhdan’s property (T) from representation theory of semi-simple Lie groups was applied in both cases to achieve partial results, and later on, both problems were solved using the (proved) Ramanujan conjecture from the theory of automorphic forms. The fact that representation theory and automorphic forms have anything to do with these problems is a surprise and a hint as well that the two questions are strongly related.
Author: Andrés Navas
Publisher: University of Chicago Press
ISBN: 0226569519
Category : Mathematics
Languages : en
Pages : 310
Get Book Here
Book Description
In recent years scholars from a variety of branches of mathematics have made several significant developments in the theory of group actions. Groups of Circle Diffeomorphisms systematically explores group actions on the simplest closed manifold, the circle. As the group of circle diffeomorphisms is an important subject in modern mathematics, this book will be of interest to those doing research in group theory, dynamical systems, low dimensional geometry and topology, and foliation theory. The book is mostly self-contained and also includes numerous complementary exercises, making it an excellent textbook for undergraduate and graduate students.
Author: Mikhail Ershov
Publisher: American Mathematical Soc.
ISBN: 1470426048
Category : Mathematics
Languages : en
Pages : 148
Get Book Here
Book Description
The authors introduce and study the class of groups graded by root systems. They prove that if is an irreducible classical root system of rank and is a group graded by , then under certain natural conditions on the grading, the union of the root subgroups is a Kazhdan subset of . As the main application of this theorem the authors prove that for any reduced irreducible classical root system of rank and a finitely generated commutative ring with , the Steinberg group and the elementary Chevalley group have property . They also show that there exists a group with property which maps onto all finite simple groups of Lie type and rank , thereby providing a “unified” proof of expansion in these groups.
Author: James Haglund
Publisher: American Mathematical Soc.
ISBN: 0821844113
Category : Mathematics
Languages : en
Pages : 178
Get Book Here
Book Description
This work contains detailed descriptions of developments in the combinatorics of the space of diagonal harmonics, a topic at the forefront of current research in algebraic combinatorics. These developments have led in turn to some surprising discoveries in the combinatorics of Macdonald polynomials.
Author: Cornelia Druţu
Publisher: American Mathematical Soc.
ISBN: 1470411040
Category : Mathematics
Languages : en
Pages : 841
Get Book Here
Book Description
The key idea in geometric group theory is to study infinite groups by endowing them with a metric and treating them as geometric spaces. This applies to many groups naturally appearing in topology, geometry, and algebra, such as fundamental groups of manifolds, groups of matrices with integer coefficients, etc. The primary focus of this book is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan's Property (T) and the Haagerup property, as well as their characterizations in terms of group actions on median spaces and spaces with walls. The book contains proofs of several fundamental results of geometric group theory, such as Gromov's theorem on groups of polynomial growth, Tits's alternative, Stallings's theorem on ends of groups, Dunwoody's accessibility theorem, the Mostow Rigidity Theorem, and quasiisometric rigidity theorems of Tukia and Schwartz. This is the first book in which geometric group theory is presented in a form accessible to advanced graduate students and young research mathematicians. It fills a big gap in the literature and will be used by researchers in geometric group theory and its applications.
Author: A. S. Kechris
Publisher: American Mathematical Soc.
ISBN: 0821848941
Category : Mathematics
Languages : en
Pages : 258
Get Book Here
Book Description
A study of ergodic, measure preserving actions of countable discrete groups on standard probability spaces. It explores a direction that emphasizes a global point of view, concentrating on the structure of the space of measure preserving actions of a given group and its associated cocycle spaces.
Author: Oleg Bogopolski
Publisher: Springer Science & Business Media
ISBN: 3764399112
Category : Mathematics
Languages : en
Pages : 318
Get Book Here
Book Description
This volume assembles several research papers in all areas of geometric and combinatorial group theory originated in the recent conferences in Dortmund and Ottawa in 2007. It contains high quality refereed articles developing new aspects of these modern and active fields in mathematics. It is also appropriate to advanced students interested in recent results at a research level.
