Coarse Geometry Of Topological Groups
DOWNLOAD
Download Coarse Geometry Of Topological Groups PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Coarse Geometry Of Topological Groups book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Coarse Geometry Of Topological Groups
DOWNLOAD
Author : Christian Rosendal
language : en
Publisher: Cambridge University Press
Release Date : 2021-12-16
Coarse Geometry Of Topological Groups written by Christian Rosendal and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-16 with Mathematics categories.
Provides a general framework for doing geometric group theory for non-locally-compact topological groups arising in mathematical practice.
An Invitation To Coarse Groups
DOWNLOAD
Author : Arielle Leitner
language : en
Publisher: Springer Nature
Release Date : 2023-12-12
An Invitation To Coarse Groups written by Arielle Leitner and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-12 with Mathematics categories.
This book lays the foundation for a theory of coarse groups: namely, sets with operations that satisfy the group axioms “up to uniformly bounded error”. These structures are the group objects in the category of coarse spaces, and arise naturally as approximate subgroups, or as coarse kernels. The first aim is to provide a standard entry-level introduction to coarse groups. Extra care has been taken to give a detailed, self-contained and accessible account of the theory. The second aim is to quickly bring the reader to the forefront of research. This is easily accomplished, as the subject is still young, and even basic questions remain unanswered. Reflecting its dual purpose, the book is divided into two parts. The first part covers the fundamentals of coarse groups and their actions. Here the theory of coarse homomorphisms, quotients and subgroups is developed, with proofs of coarse versions of the isomorphism theorems, and it is shown how coarse actions are related to fundamental aspects of geometric group theory. The second part, which is less self-contained, is an invitation to further research, where each thread leads to open questions of varying depth and difficulty. Among other topics, it explores coarse group structures on set-groups, groups of coarse automorphisms and spaces of controlled maps. The main focus is on connections between the theory of coarse groups and classical subjects, including: number theory; the study of bi-invariant metrics on groups; quasimorphisms and stable commutator length; groups of outer automorphisms; and topological groups and their actions. The book will primarily be of interest to researchers and graduate students in geometric group theory, topology, category theory and functional analysis, but some parts will also be accessible to advanced undergraduates.
Metric Geometry Of Locally Compact Groups
DOWNLOAD
Author : Yves Cornulier
language : en
Publisher: European Mathematical Society
Release Date : 2016
Metric Geometry Of Locally Compact Groups written by Yves Cornulier and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Mathematics categories.
The main aim of this book is the study of locally compact groups from a geometric perspective, with an emphasis on appropriate metrics that can be defined on them. The approach has been successful for finitely generated groups and can be favorably extended to locally compact groups. Parts of the book address the coarse geometry of metric spaces, where ``coarse'' refers to that part of geometry concerning properties that can be formulated in terms of large distances only. This point of view is instrumental in studying locally compact groups. Basic results in the subject are exposed with complete proofs; others are stated with appropriate references. Most importantly, the development of the theory is illustrated by numerous examples, including matrix groups with entries in the the field of real or complex numbers, or other locally compact fields such as $p$-adic fields, isometry groups of various metric spaces, and last but not least, discrete groups themselves. The book is aimed at graduate students, advanced undergraduate students, and mathematicians seeking some introduction to coarse geometry and locally compact groups.
Coarse Geometry And Randomness
DOWNLOAD
Author : Itai Benjamini
language : en
Publisher: Springer
Release Date : 2013-12-02
Coarse Geometry And Randomness written by Itai Benjamini and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-02 with Mathematics categories.
These lecture notes study the interplay between randomness and geometry of graphs. The first part of the notes reviews several basic geometric concepts, before moving on to examine the manifestation of the underlying geometry in the behavior of random processes, mostly percolation and random walk. The study of the geometry of infinite vertex transitive graphs, and of Cayley graphs in particular, is fairly well developed. One goal of these notes is to point to some random metric spaces modeled by graphs that turn out to be somewhat exotic, that is, they admit a combination of properties not encountered in the vertex transitive world. These include percolation clusters on vertex transitive graphs, critical clusters, local and scaling limits of graphs, long range percolation, CCCP graphs obtained by contracting percolation clusters on graphs, and stationary random graphs, including the uniform infinite planar triangulation (UIPT) and the stochastic hyperbolic planar quadrangulation (SHIQ).
In The Tradition Of Thurston
DOWNLOAD
Author : Ken’ichi Ohshika
language : en
Publisher: Springer Nature
Release Date : 2020-12-07
In The Tradition Of Thurston written by Ken’ichi Ohshika and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-07 with Mathematics categories.
This book consists of 16 surveys on Thurston's work and its later development. The authors are mathematicians who were strongly influenced by Thurston's publications and ideas. The subjects discussed include, among others, knot theory, the topology of 3-manifolds, circle packings, complex projective structures, hyperbolic geometry, Kleinian groups, foliations, mapping class groups, Teichmüller theory, anti-de Sitter geometry, and co-Minkowski geometry. The book is addressed to researchers and students who want to learn about Thurston’s wide-ranging mathematical ideas and their impact. At the same time, it is a tribute to Thurston, one of the greatest geometers of all time, whose work extended over many fields in mathematics and who had a unique way of perceiving forms and patterns, and of communicating and writing mathematics.
Index Theory Coarse Geometry And Topology Of Manifolds
DOWNLOAD
Author : John Roe
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Index Theory Coarse Geometry And Topology Of Manifolds written by John Roe and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
Lecture notes from the conference held Aug. 1995 in Boulder, Colo.
Higher Index Theory
DOWNLOAD
Author : Rufus Willett
language : en
Publisher: Cambridge University Press
Release Date : 2020-07-02
Higher Index Theory written by Rufus Willett and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-02 with Mathematics categories.
A friendly introduction to higher index theory, a rapidly-developing subject at the intersection of geometry, topology and operator algebras. A well-balanced combination of introductory material (with exercises), cutting-edge developments and references to the wider literature make this book a valuable guide for graduate students and experts alike.
Topological Methods In Group Theory
DOWNLOAD
Author : Ross Geoghegan
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-27
Topological Methods In Group Theory written by Ross Geoghegan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-27 with Mathematics categories.
This book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit.
A Course In Metric Geometry
DOWNLOAD
Author : Dmitri Burago
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
A Course In Metric Geometry written by Dmitri Burago and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
"Metric geometry" is an approach to geometry based on the notion of length on a topological space. This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations. The objective of this graduate textbook is twofold: to give a detailed exposition of basic notions and techniques used in the theory of length spaces, and, more generally, to offer an elementary introduction into a broad variety of geometrical topics related to the notion of distance, including Riemannian and Carnot-Caratheodory metrics, the hyperbolic plane, distance-volume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (non-positively and non-negatively curved spaces).
Homotopy Theory With Bornological Coarse Spaces
DOWNLOAD
Author : Ulrich Bunke
language : en
Publisher: Springer Nature
Release Date : 2020-09-03
Homotopy Theory With Bornological Coarse Spaces written by Ulrich Bunke and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-03 with Mathematics categories.
Providing a new approach to assembly maps, this book develops the foundations of coarse homotopy using the language of infinity categories. It introduces the category of bornological coarse spaces and the notion of a coarse homology theory, and further constructs the universal coarse homology theory. Hybrid structures are introduced as a tool to connect large-scale with small-scale geometry, and are then employed to describe the coarse motives of bornological coarse spaces of finite asymptotic dimension. The remainder of the book is devoted to the construction of examples of coarse homology theories, including an account of the coarsification of locally finite homology theories and of coarse K-theory. Thereby it develops background material about locally finite homology theories and C*-categories. The book is intended for advanced graduate students and researchers who want to learn about the homotopy-theoretical aspects of large scale geometry via the theory of infinity categories.