Titlebook: Geometric Group Theory; An Introduction Clara Löh Textbook 2017 Springer International Publishing AG 2017 MSC 2010 20F65 20F67 20F69 20F05

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Quasi-isometryaphs: If . is a group and . is a generating set of ., then the paths in the associated Cayley graph Cay(.) induce a metric on ., the word metric with respect to the generating set .; unfortunately, in general, this metric depends on the chosen generating set.

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Ends and boundariesof geometry at infinity (or a “boundary”) should assign “nice” topological spaces to given metric spaces that reect the behaviour of the given metric spaces “far out”, and it should turn quasi-isometries of metric spaces into homeomorphisms of the corresponding topological spaces; more concisely, a

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0172-5939 oundary 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..978-3-319-72253-5978-3-319-72254-2Series ISSN 0172-5939 Series E-ISSN 2191-6675

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Textbook 2017e 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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