Two-dimensional homotopy and combinatorial group theory / edited by Cynthia Hog-Angeloni, Wolfgang Metzler and Allan J. Sieradski
Language: English
Published by Cambridge : Cambridge University Press, 1993
Series: Book 166 of 387 - London Mathematical Society Lecture Notes
- First Edition
- Softcover
- Used
Condition: Used
£ 51.56
Quantity: 1 available
Add to basketItem description from seller
Very good paperback copy; edges slightly dust-dulled and nicked. Remains particularly well-preserved overall; tight, bright, and clean. Physical description; xi, 412 pages. Notes; Includes bibliographical references (p. 381-407) and index. Contents; Cover; Title; Copyright; Contents; Editors' Preface; Addresses of Authors; I Geometric Aspects of Two-Dimensional Complexes; 1 Complexes of Low Dimensions and Group Presentations . . .; 1.1 Inductive construction of CW-complexes; 1.2 Questions of subdivision and triangulation; 1.3 Reading off presentations for TTI of a CW-complex; 1.4 PLCW-complexes; 2 Simple-Homotopy and Low Dimensions; 2.1 A survey on geometric simple-homotopy; 2.2 Some examples; 2.3 3-deformation types and (Q**-transformations; 3 P.L. Embeddings of 2-Complexes into Manifolds; 3.1 3-dimensional thickenings. 3.2 4- and 5-dimensional thickenings4 Three Conjectures and Further Problems; 4.1 (Generalized) Andrews-Curtis conjecture; 4.2 Zeeman collapsing conjecture; 4.3 Whitehead asphericity conjecture as a special problem of dimension 2; 4.4 Further open questions; II Algebraic Topology for Two Dimensional Complexes; 1 Techniques in Homotopy; 1.1 Simplicial Techniques; 1.2 Combinatorial Maps; 2 Homotopy Groups for 2-Complexes 62; 2.1 Fundamental sequence for a 2-complex K; 2.2 II(K) and the homotopy type of a 2-complex K; 3 Equivariant World for 2-Complexes; 3.1 Hurewicz Isomorphism Theorems. 3.2 Two Dimensional Equivariant World4 Mac Lane-Whitehead Algebraic Types; 4.1 Homology and Cohomology of Groups; 4.2 Maps between 2-complexes; III Homotopy and Homology Classification of 2-Complexes; 1 Bias Invariant & Homology Classification; 1.1 Bias as a homotopy obstruction; 1.2 Bias as the complete homology obstruction; 1.3 Homotopy distinction of twisted presentations; 2 Classifications for Finite Abelian TTI Ill; 2.1 The Browning obstruction group; 2.2 Homotopy classification for finite abelian TTI; 3 Classifications for Non-Finite TTI (with Cynthia Hog-Angeloni); 3.1 Infinite groups. generalized Browning invariant3.2 Results when TTI is a free product of cyclic groups; 3.3 Trees of homotopy types, simple-homotopy types, and 3_deformation types; 3.4 Problems for Chapter III; IV Crossed Modules and n2 Homotopy Modules; 1 Introduction; 2 Crossed and Precrossed Modules; 2.1 Free crossed modules; 2.2 A characterization of free crossed modules; 2.3 Projective crossed modules; 2.4 Two-complexes and projective crossed modules; 2.5 The kernel of a projective crossed module; 3 On the Second Homotopy Module of a 2-Complex; 3.1 Coproducts of crossed modules; 3.2 A special case. 3.3 On the kernel of a coproduct of crossed modules3.4 Computing ?2 from subcomplexes; 4 Identity Properties; 4.1 H-Cockcroft complexes; 4.2 Characterizing Cockcroft complexes; 4.3 Minimal subgroups; V Calculating Generators of n2; 1 The Theory of Pictures; 1.1 Pictures; 1.2 Homotopy theory of pictures; 2 Generation of ?2; 2.1 Asphericity; 2.2 A Dehn algorithm for ?2; 2.3 Subpresentations; 3 Applications and Results; 3.1 Universal group of a family of subgroups; 3.2 Generalized graphs of groups; 3.3 Split extensions; 3.4 Iterative constructions; 3.5 The Steinberg group and K3 of a ring. 3.6 Presentations defined using simplicial complexes. Subjects; Homotopy theory. Combinatorial group theory. Low-dimensional topology. 1 Kg.…
Seller Inventory # 432888
- Title
- Two-dimensional homotopy and combinatorial group theory / edited by Cynthia Hog-Angeloni, Wolfgang Metzler and Allan J. Sieradski
- Author
- Hog-Angeloni, Cynthia [editor]
- Publisher
- Cambridge : Cambridge University Press
- Publication year
- 1993
- Binding
- Soft cover
- Language
- English
- ISBN 10
- 0521447003
- ISBN 13
- 9780521447003
- Edition
- First Edition.
- Item weight
- 1 kilogram
- Series
- Book 166 of 387: London Mathematical Society Lecture Notes
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