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Geometric group theory [electronic resource] : an introduction

Geometric group theory [electronic resource] : an introduction

Material type
E-Book(소장)
Personal Author
Löh, Clara.
Title Statement
Geometric group theory [electronic resource] : an introduction / Clara Löh.
Publication, Distribution, etc
Cham :   Springer,   c2017.  
Physical Medium
1 online resource (xi, 389 p.) : ill. (some col.).
Series Statement
Universitext,0172-5939
ISBN
9783319722535 9783319722542 (eBook)
요약
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.
General Note
Title from e-Book title page.  
Content Notes
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.
Bibliography, Etc. Note
Includes bibliographical references and indexes.
이용가능한 다른형태자료
Issued also as a book.  
Subject Added Entry-Topical Term
Group theory. Global differential geometry. Cell aggregation --Mathematics.
Short cut
URL
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020 ▼a 9783319722535
020 ▼a 9783319722542 (eBook)
040 ▼a 211009 ▼c 211009 ▼d 211009
050 4 ▼a QA174-183
082 0 4 ▼a 512.2 ▼2 23
084 ▼a 512.2 ▼2 DDCK
090 ▼a 512.2
100 1 ▼a Löh, Clara.
245 1 0 ▼a Geometric group theory ▼h [electronic resource] : ▼b an introduction / ▼c Clara Löh.
260 ▼a Cham : ▼b Springer, ▼c c2017.
300 ▼a 1 online resource (xi, 389 p.) : ▼b ill. (some col.).
490 1 ▼a Universitext, ▼x 0172-5939
500 ▼a Title from e-Book title page.
504 ▼a Includes bibliographical references and indexes.
505 0 ▼a 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.
520 ▼a 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.
530 ▼a Issued also as a book.
538 ▼a Mode of access: World Wide Web.
650 0 ▼a Group theory.
650 0 ▼a Global differential geometry.
650 0 ▼a Cell aggregation ▼x Mathematics.
830 0 ▼a Universitext.
856 4 0 ▼u https://oca.korea.ac.kr/link.n2s?url=https://doi.org/10.1007/978-3-319-72254-2
945 ▼a KLPA
991 ▼a E-Book(소장)

Holdings Information

No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Main Library/e-Book Collection/ Call Number CR 512.2 Accession No. E14014667 Availability Loan can not(reference room) Due Date Make a Reservation Service M

Contents information

Table of Contents

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.

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