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010   $a3-319-72254-9
024 7 $a10.1007/978-3-319-72254-2
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035   $a(DE-He213)978-3-319-72254-2
035   $a(MiAaPQ)EBC6312482
035   $a(MiAaPQ)EBC5576927
035   $a(Au-PeEL)EBL5576927
035   $a(OCoLC)1017988852
035   $a(PPN)222228199
035   $a(EXLCZ)994100000001381593
100   $a20171220d2017      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aGeometric Group Theory $eAn Introduction /$fby Clara Löh
205   $a1st ed. 2017.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017.
215   $a1 online resource (XI, 389 p. 119 illus., 100 illus. in color.) 
225 1 $aUniversitext,$x0172-5939
311   $a3-319-72253-0 
327   $a1 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.
330   $aInspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.
410  0$aUniversitext,$x0172-5939
606   $aGroup theory
606   $aDifferential geometry
606   $aHyperbolic geometry
606   $aManifolds (Mathematics)
606   $aComplex manifolds
606   $aGraph theory
606   $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078
606   $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022
606   $aHyperbolic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21030
606   $aManifolds and Cell Complexes (incl. Diff.Topology)$3https://scigraph.springernature.com/ontologies/product-market-codes/M28027
606   $aGraph Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M29020
615  0$aGroup theory.
615  0$aDifferential geometry.
615  0$aHyperbolic geometry.
615  0$aManifolds (Mathematics).
615  0$aComplex manifolds.
615  0$aGraph theory.
615 14$aGroup Theory and Generalizations.
615 24$aDifferential Geometry.
615 24$aHyperbolic Geometry.
615 24$aManifolds and Cell Complexes (incl. Diff.Topology).
615 24$aGraph Theory.
676   $a512.2
700   $aLöh$b Clara$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767630
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910254295903321
996   $aGeometric Group Theory$91563065
997   $aUNINA