03620nam a22005655i 4500 978-3-319-72254-2 DE-He213 20210618235654.0 cr nn 008mamaa 171220s2017 gw | s |||| 0|eng d 9783319722542 978-3-319-72254-2 10.1007/978-3-319-72254-2 doi QA174-183 PBG bicssc MAT002010 bisacsh PBG thema 512.2 23 Löh, Clara. author. aut http://id.loc.gov/vocabulary/relators/aut Geometric Group Theory [electronic resource] : An Introduction / by Clara Löh. 1st ed. 2017. Cham : Springer International Publishing : Imprint: Springer, 2017. XI, 389 p. 119 illus., 100 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Universitext, 0172-5939 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. Group theory. Differential geometry. Hyperbolic geometry. Manifolds (Mathematics). Complex manifolds. Graph theory. Group Theory and Generalizations. https://scigraph.springernature.com/ontologies/product-market-codes/M11078 Differential Geometry. https://scigraph.springernature.com/ontologies/product-market-codes/M21022 Hyperbolic Geometry. https://scigraph.springernature.com/ontologies/product-market-codes/M21030 Manifolds and Cell Complexes (incl. Diff.Topology). https://scigraph.springernature.com/ontologies/product-market-codes/M28027 Graph Theory. https://scigraph.springernature.com/ontologies/product-market-codes/M29020 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783319722535 Printed edition: 9783319722559 Universitext, 0172-5939 https://doi.org/10.1007/978-3-319-72254-2 ZDB-2-SMA ZDB-2-SXMS Mathematics and Statistics (SpringerNature-11649) Mathematics and Statistics (R0) (SpringerNature-43713)