03899nam 22007215 450 991025429590332120200629210055.03-319-72254-910.1007/978-3-319-72254-2(CKB)4100000001381593(DE-He213)978-3-319-72254-2(MiAaPQ)EBC6312482(MiAaPQ)EBC5576927(Au-PeEL)EBL5576927(OCoLC)1017988852(PPN)222228199(EXLCZ)99410000000138159320171220d2017 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierGeometric Group Theory An Introduction /by Clara Löh1st ed. 2017.Cham :Springer International Publishing :Imprint: Springer,2017.1 online resource (XI, 389 p. 119 illus., 100 illus. in color.) Universitext,0172-59393-319-72253-0 1 Introduction -- Part I Groups -- 2 Generating groups -- Part II Groups > Geometry -- 3 Cayley graphs -- 4 Group actions -- 5 Quasi-isometry -- Part III Geometry of groups -- 6 Growth types of groups -- 7 Hyperbolic groups -- 8 Ends and boundaries -- 9 Amenable groups -- Part IV Reference material -- A Appendix -- Bibliography -- Indices.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.Universitext,0172-5939Group theoryGeometry, DifferentialGeometry, HyperbolicManifolds (Mathematics)Complex manifoldsGraph theoryGroup Theory and Generalizationshttps://scigraph.springernature.com/ontologies/product-market-codes/M11078Differential Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21022Hyperbolic Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21030Manifolds and Cell Complexes (incl. Diff.Topology)https://scigraph.springernature.com/ontologies/product-market-codes/M28027Graph Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M29020Group theory.Geometry, Differential.Geometry, Hyperbolic.Manifolds (Mathematics)Complex manifolds.Graph theory.Group Theory and Generalizations.Differential Geometry.Hyperbolic Geometry.Manifolds and Cell Complexes (incl. Diff.Topology).Graph Theory.512.2Löh Claraauthttp://id.loc.gov/vocabulary/relators/aut767630MiAaPQMiAaPQMiAaPQBOOK9910254295903321Geometric Group Theory1563065UNINA