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

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,Wenn nur die Kunden nicht w?ren,aphs: 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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Obstacle

Group actionsetric aspect of groups by looking at group actions, which can be viewed as a generalisation of seeing groups as symmetry groups.We start by recalling some basic concepts about group actions (Chapter 4.1).

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Ends and boundariesboundary mechanism should be a functor promoting maps and properties from the wild world of quasi-isometries to the potentially tamer world of topology. In particular, boundaries are quasi-isometry invariants; surprisingly, in many cases, boundaries know enough about the underlying metric spaces to allow for interesting rigidity results.

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0172-5939 rowth, hyperbolicity, boundary constructions and amenability.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

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cluster

Generating groupsl present basic construction principles that allow us to generate interesting examples of groups. This includes the description of groups in terms of generators and relations and the iterative construction of groups via semi-direct products, amalgamated free products, and HNN-extensions.

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Group actionsetric aspect of groups by looking at group actions, which can be viewed as a generalisation of seeing groups as symmetry groups.We start by recalling some basic concepts about group actions (Chapter 4.1).