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Geometric group theory [electronic resource] : an introduction

Geometric group theory [electronic resource] : an introduction

자료유형
E-Book(소장)
개인저자
Löh, Clara.
서명 / 저자사항
Geometric group theory [electronic resource] : an introduction / Clara Löh.
발행사항
Cham :   Springer,   c2017.  
형태사항
1 online resource (xi, 389 p.) : ill. (some col.).
총서사항
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.
일반주기
Title from e-Book title page.  
내용주기
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.
서지주기
Includes bibliographical references and indexes.
이용가능한 다른형태자료
Issued also as a book.  
일반주제명
Group theory. Global differential geometry. Cell aggregation --Mathematics.
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020 ▼a 9783319722535
020 ▼a 9783319722542 (eBook)
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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)

소장정보

No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 중앙도서관/e-Book 컬렉션/ 청구기호 CR 512.2 등록번호 E14014667 도서상태 대출불가(열람가능) 반납예정일 예약 서비스 M

컨텐츠정보

목차

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.

관련분야 신착자료

Aluffi, Paolo (2021)