Kazhdan's Property (T) and Related Properties Locally Compact and Discrete Groups
Author: Annabel Deutsch
Publisher:
Published: 1992
Total Pages: 0
ISBN-13:
DOWNLOAD EBOOKPosts
Kazhdan's Property (T) and Related Properties Locally Compact and Discrete Groups
Author: Annabel Deutsch
Publisher:
Published: 1992
Total Pages:
ISBN-13:
DOWNLOAD EBOOKKazhdan's Property (T)
Author: Bekka M Bachir La Harpe Pierre de Valette Alain
Publisher:
Published: 2014-05-14
Total Pages: 488
ISBN-13: 9780511395116
DOWNLOAD EBOOKA comprehensive introduction to the role of Property (T), with applications to an amazing number of fields within mathematics.
Locally Compact Groups
Author: Markus Stroppel
Publisher: European Mathematical Society
Published: 2006
Total Pages: 320
ISBN-13: 9783037190166
DOWNLOAD EBOOKLocally compact groups play an important role in many areas of mathematics as well as in physics. The class of locally compact groups admits a strong structure theory, which allows to reduce many problems to groups constructed in various ways from the additive group of real numbers, the classical linear groups and from finite groups. The book gives a systematic and detailed introduction to the highlights of that theory. In the beginning, a review of fundamental tools from topology and the elementary theory of topological groups and transformation groups is presented. Completions, Haar integral, applications to linear representations culminating in the Peter-Weyl Theorem are treated. Pontryagin duality for locally compact Abelian groups forms a central topic of the book. Applications are given, including results about the structure of locally compact Abelian groups, and a structure theory for locally compact rings leading to the classification of locally compact fields. Topological semigroups are discussed in a separate chapter, with special attention to their relations to groups. The last chapter reviews results related to Hilbert's Fifth Problem, with the focus on structural results for non-Abelian connected locally compact groups that can be derived using approximation by Lie groups. The book is self-contained and is addressed to advanced undergraduate or graduate students in mathematics or physics. It can be used for one-semester courses on topological groups, on locally compact Abelian groups, or on topological algebra. Suggestions on course design are given in the preface. Each chapter is accompanied by a set of exercises that have been tested in classes.
New Directions in Locally Compact Groups
Author: Pierre-Emmanuel Caprace
Publisher: Cambridge University Press
Published: 2018-02-08
Total Pages: 367
ISBN-13: 1108349544
DOWNLOAD EBOOKThis collection of expository articles by a range of established experts and newer researchers provides an overview of the recent developments in the theory of locally compact groups. It includes introductory articles on totally disconnected locally compact groups, profinite groups, p-adic Lie groups and the metric geometry of locally compact groups. Concrete examples, including groups acting on trees and Neretin groups, are discussed in detail. An outline of the emerging structure theory of locally compact groups beyond the connected case is presented through three complementary approaches: Willis' theory of the scale function, global decompositions by means of subnormal series, and the local approach relying on the structure lattice. An introduction to lattices, invariant random subgroups and L2-invariants, and a brief account of the Burger–Mozes construction of simple lattices are also included. A final chapter collects various problems suggesting future research directions.
Dynamics: Topology and Numbers
Author: Pieter Moree
Publisher: American Mathematical Soc.
Published: 2020-02-12
Total Pages: 347
ISBN-13: 147045100X
DOWNLOAD EBOOKThis volume contains the proceedings of the conference Dynamics: Topology and Numbers, held from July 2–6, 2018, at the Max Planck Institute for Mathematics, Bonn, Germany. The papers cover diverse fields of mathematics with a unifying theme of relation to dynamical systems. These include arithmetic geometry, flat geometry, complex dynamics, graph theory, relations to number theory, and topological dynamics. The volume is dedicated to the memory of Sergiy Kolyada and also contains some personal accounts of his life and mathematics.
Expansion in Finite Simple Groups of Lie Type
Author: Terence Tao
Publisher: American Mathematical Soc.
Published: 2015-04-16
Total Pages: 319
ISBN-13: 1470421968
DOWNLOAD EBOOKExpander graphs are an important tool in theoretical computer science, geometric group theory, probability, and number theory. Furthermore, the techniques used to rigorously establish the expansion property of a graph draw from such diverse areas of mathematics as representation theory, algebraic geometry, and arithmetic combinatorics. This text focuses on the latter topic in the important case of Cayley graphs on finite groups of Lie type, developing tools such as Kazhdan's property (T), quasirandomness, product estimates, escape from subvarieties, and the Balog-Szemerédi-Gowers lemma. Applications to the affine sieve of Bourgain, Gamburd, and Sarnak are also given. The material is largely self-contained, with additional sections on the general theory of expanders, spectral theory, Lie theory, and the Lang-Weil bound, as well as numerous exercises and other optional material.
Topological Groups
Author: Source Wikipedia
Publisher: University-Press.org
Published: 2013-09
Total Pages: 90
ISBN-13: 9781230589541
DOWNLOAD EBOOKPlease note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 43. Chapters: Adelic algebraic group, Almost periodic function, Amenable group, Bohr compactification, Cantor cube, Chabauty topology, Circle group, Compactly generated group, Compact group, Covering group, Free regular set, Fundamental domain, Haar measure, Hilbert-Smith conjecture, Homeomorphism group, Homogeneous space, Identity component, Kazhdan's property (T), Kronecker's theorem, Locally compact group, Locally profinite group, Loop group, Mautner's lemma, Maximal compact subgroup, Monothetic group, Noncommutative harmonic analysis, No small subgroup, One-parameter group, Peter-Weyl theorem, Pontryagin duality, Principal homogeneous space, Pro-p group, Properly discontinuous action, Prosolvable group, Restricted product, Schwartz-Bruhat function, Solenoid (mathematics), System of imprimitivity, Tannaka-Krein duality, Topological abelian group, Topological group, Topological semigroup, Totally disconnected group, Von Neumann conjecture. Excerpt: In mathematics, specifically in harmonic analysis and the theory of topological groups, Pontryagin duality explains the general properties of the Fourier transform on locally compact groups, such as R, the circle or finite cyclic groups. The Pontryagin duality theorem itself states that locally compact groups identify naturally with their bidual. The subject is named after Lev Semenovich Pontryagin who laid down the foundations for the theory of locally compact abelian groups and their duality during his early mathematical works in 1934. Pontryagin's treatment relied on the group being second-countable and either compact or discrete. This was improved to cover the general locally compact abelian groups by Egbert van Kampen in 1935 and Andre Weil in 1940. Pontryagin duality places in a unified context a number of observations about functions on the real line or on finite...
Directions in Infinite Graph Theory and Combinatorics
Author: R. Diestel
Publisher: Elsevier
Published: 2016-06-06
Total Pages: 392
ISBN-13: 148329479X
DOWNLOAD EBOOKThis book has arisen from a colloquium held at St. John's College, Cambridge, in July 1989, which brought together most of today's leading experts in the field of infinite graph theory and combinatorics. This was the first such meeting ever held, and its aim was to assess the state of the art in the discipline, to consider its links with other parts of mathematics, and to discuss possible directions for future development. This volume reflects the Cambridge meeting in both level and scope. It contains research papers as well as expository surveys of particular areas. Together they offer a comprehensive portrait of infinite graph theory and combinatorics, which should be particularly attractive to anyone new to the discipline.
Locally Compact Property a Groups
Author: Amanda Harsy
Publisher: LAP Lambert Academic Publishing
Published: 2014-09-15
Total Pages: 68
ISBN-13: 9783659608100
DOWNLOAD EBOOKIn 1970, Serge Novikov made a statement which is now called, "The Novikov Conjecture" and is considered to be one of the major open problems in topology. This statement was motivated by the endeavor to understand manifolds of arbitrary dimensions by relating the surgery map with the homology of the fundamental group of the manifold, which becomes difficult for manifolds of dimension greater than two. This Conjecture is interesting because it comes up in problems in many different branches of mathematics like algebra, analysis, K-theory, differential geometry, operator algebras and representation theory. Yu later proved the Novikov Conjecture holds for all closed manifolds with discrete fundamental groups that are coarsely embeddable into a Hilbert space. The class of groups that are uniformly embeddable into Hilbert Spaces includes groups of Property A which were introduced by Yu. In fact, Property A is generally a property of metric spaces and is stable under quasi-isometry. In this dissertation, a new version of Yu's Property A in the case of locally compact groups is introduced. This new notion of Property A coincides with Yu's Property A in the case of discrete groups.
