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Geometric group theory: an introduction

Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be p...

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Autor principal: Löh, Clara
Lenguaje:eng
Publicado: Springer 2017
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-319-72254-2
http://cds.cern.ch/record/2300449
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author Löh, Clara
author_facet Löh, Clara
author_sort Löh, Clara
collection CERN
description Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.
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spelling cern-23004492021-04-21T18:56:53Zdoi:10.1007/978-3-319-72254-2http://cds.cern.ch/record/2300449engLöh, ClaraGeometric group theory: an introductionMathematical Physics and MathematicsInspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.Springeroai:cds.cern.ch:23004492017
spellingShingle Mathematical Physics and Mathematics
Löh, Clara
Geometric group theory: an introduction
title Geometric group theory: an introduction
title_full Geometric group theory: an introduction
title_fullStr Geometric group theory: an introduction
title_full_unstemmed Geometric group theory: an introduction
title_short Geometric group theory: an introduction
title_sort geometric group theory: an introduction
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-319-72254-2
http://cds.cern.ch/record/2300449
work_keys_str_mv AT lohclara geometricgrouptheoryanintroduction