Coarse Geometry of Topological Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Coarse Geometry of Topological Groups write by Christian Rosendal. This book was released on 2021-12-16. Coarse Geometry of Topological Groups available in PDF, EPUB and Kindle. Provides a general framework for doing geometric group theory for non-locally-compact topological groups arising in mathematical practice.
Coarse Geometry of Topological Groups
Coarse Geometry of Topological Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Coarse Geometry of Topological Groups write by Christian Rosendal. This book was released on 2021-12-16. Coarse Geometry of Topological Groups available in PDF, EPUB and Kindle. This book provides a general framework for doing geometric group theory for many non-locally-compact topological transformation groups that arise in mathematical practice, including homeomorphism and diffeomorphism groups of manifolds, isometry groups of separable metric spaces and automorphism groups of countable structures. Using Roe's framework of coarse structures and spaces, the author defines a natural coarse geometric structure on all topological groups. This structure is accessible to investigation, especially in the case of Polish groups, and often has an explicit description, generalising well-known structures in familiar cases including finitely generated discrete groups, compactly generated locally compact groups and Banach spaces. In most cases, the coarse geometric structure is metrisable and may even be refined to a canonical quasimetric structure on the group. The book contains many worked examples and sufficient introductory material to be accessible to beginning graduate students. An appendix outlines several open problems in this young and rich theory.
Lectures on Coarse Geometry
Lectures on Coarse Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Coarse Geometry write by John Roe. This book was released on 2003. Lectures on Coarse Geometry available in PDF, EPUB and Kindle. Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This book provides a general perspective on coarse structures. It discusses results on asymptotic dimension and uniform embeddings into Hilbert space.
A Course on Topological Groups
A Course on Topological Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Course on Topological Groups write by K. Chandrasekharan. This book was released on 1996-01-01. A Course on Topological Groups available in PDF, EPUB and Kindle.
An Invitation to Coarse Groups
An Invitation to Coarse Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Invitation to Coarse Groups write by Arielle Leitner. This book was released on 2024-01-13. An Invitation to Coarse Groups available in PDF, EPUB and Kindle. 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.
