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03058aam a2200409 i 4500 001 BCFEC1D6A5B811ECBC4A196C2DECA4DB 003 SILO 005 20220317010139 008 210311t20212021enka b 001 0deng 010 $a 2021003166 020 $a 110884247X 020 $a 9781108842471 035 $a (OCoLC)1243012855 040 $a LBSOR/DLC $b eng $e rda $c DLC $d OCLCO $d YDX $d OCLCF $d UKMGB $d YDX $d OCLCO $d NUI $d SILO 042 $a pcc 100 1 $a Rosendal, Christian, $e author. 245 10 $a Coarse geometry of topological groups / $c Christian Rosendal. 264 1 $a Cambridge, United Kingdom ; $b Cambridge University Press, $c 2021. 300 $a ix, 297 pages : $b illustrations ; $c 24 cm. 490 1 $a Cambridge tracts in mathematics ; $v 223 504 $a Includes bibliographical references (pages 289-294) and index. 505 0 $a Coarse structure and metrisability -- Structure theory -- Sections, cocycles and group extensions -- Polish groups of bounded geometry -- Automorphism groups of countable structures -- Zappa-SzeÌp products. 520 $a "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 several familiar cases such as 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 plenty of 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"--Provided by publisher. 650 0 $a Geometric group theory. 650 0 $a Topological groups. 650 0 $a Transformation groups. 650 0 $a Polish spaces (Mathematics) 650 7 $a Geometric group theory. $2 fast $0 (OCoLC)fst00940833 650 7 $a Polish spaces (Mathematics) $2 fast $0 (OCoLC)fst01069157 650 7 $a Topological groups. $2 fast $0 (OCoLC)fst01152684 650 7 $a Transformation groups. $2 fast $0 (OCoLC)fst01154652 776 08 $i Online version: $a Rosendal, Christian. $t Coarse geometry of topological groups $d Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2021 $z 9781108903547 $w (DLC) 2021003167 773 18 $w 990007725630202771 $g no:31858071535151 830 0 $a Cambridge tracts in mathematics ; $v 223. 941 $a 1 952 $l OVUX522 $d 20231117021325.0 956 $a http://locator.silo.lib.ia.us/search.cgi?index_0=id&term_0=BCFEC1D6A5B811ECBC4A196C2DECA4DBInitiate Another SILO Locator Search