Coarse Geometry of Topological Groups (Cambridge Tracts in Mathematics, Series Number 223) free ebook download.

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Coarse Geometry of Topological Groups (Cambridge Tracts in Mathematics, Series Number 223) free ebook download

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Author(s):	Christian Rosendal

Date:	2021	Format:	pdf	Language:	English	ISBN/ASIN:	110884247X
Pages:	200	OCR:		Quality:		ISBN13:
Uploader:	alex21s	Upload Date:	3/15/2022 8:30:16 PM

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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.
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Tags: Cambridge Coarse Geometry Groups Mathematics Number Topological Tracts

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