Two-dimensional homotopy and combinatorial group theory /:
Basic work on two-dimensional homotopy theory dates back to K. Reidemeister and J.H.C. Whitehead. Much work in this area has been done since then, and this book considers the current state of knowledge in all the aspects of the subject. The editors start with introductory chapters on low-dimensional...
Gespeichert in:
| Weitere Verfasser: | , , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York, NY :
Cambridge University Press,
1993.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
197. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Basic work on two-dimensional homotopy theory dates back to K. Reidemeister and J.H.C. Whitehead. Much work in this area has been done since then, and this book considers the current state of knowledge in all the aspects of the subject. The editors start with introductory chapters on low-dimensional topology, covering both the geometric and algebraic sides of the subject, the latter including crossed modules, Reidemeister-Peiffer identities, and a concrete and modern discussion of Whitehead's algebraic classification of 2-dimensional homotopy types. Further chapters have been skilfully selected and woven together to form a coherent picture. The latest algebraic results and their applications to 3- and 4-dimensional manifolds are dealt with. The geometric nature of the subject is illustrated to the full by over 100 diagrams. Final chapters summarize and contribute to the present status of the conjectures of Zeeman, Whitehead, and Andrews-Curtis. No other book covers all these topics. Some of the material here has been used in courses, making this book valuable for anyone with an interest in two-dimensional homotopy theory, from graduate students to research workers. |
| Beschreibung: | 1 online resource (xi, 412 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 381-407) and index. |
| ISBN: | 9781107361935 1107361931 9780511629358 0511629354 |
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| 520 | |a Basic work on two-dimensional homotopy theory dates back to K. Reidemeister and J.H.C. Whitehead. Much work in this area has been done since then, and this book considers the current state of knowledge in all the aspects of the subject. The editors start with introductory chapters on low-dimensional topology, covering both the geometric and algebraic sides of the subject, the latter including crossed modules, Reidemeister-Peiffer identities, and a concrete and modern discussion of Whitehead's algebraic classification of 2-dimensional homotopy types. Further chapters have been skilfully selected and woven together to form a coherent picture. The latest algebraic results and their applications to 3- and 4-dimensional manifolds are dealt with. The geometric nature of the subject is illustrated to the full by over 100 diagrams. Final chapters summarize and contribute to the present status of the conjectures of Zeeman, Whitehead, and Andrews-Curtis. No other book covers all these topics. Some of the material here has been used in courses, making this book valuable for anyone with an interest in two-dimensional homotopy theory, from graduate students to research workers. | ||
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 650 | 0 | |a Homotopy theory. |0 http://id.loc.gov/authorities/subjects/sh85061803 | |
| 650 | 0 | |a Combinatorial group theory. |0 http://id.loc.gov/authorities/subjects/sh85028806 | |
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| 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 |
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| id | ZDB-4-EBA-ocn836848805 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:16Z |
| institution | BVB |
| isbn | 9781107361935 1107361931 9780511629358 0511629354 |
| language | English |
| oclc_num | 836848805 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xi, 412 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society lecture note series ; |
| spelling | Two-dimensional homotopy and combinatorial group theory / edited by Cynthia Hog-Angeloni, Wolfgang Metzler and Allan J. Sieradski. Cambridge ; New York, NY : Cambridge University Press, 1993. 1 online resource (xi, 412 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 197 Includes bibliographical references (pages 381-407) and index. Print version record. Basic work on two-dimensional homotopy theory dates back to K. Reidemeister and J.H.C. Whitehead. Much work in this area has been done since then, and this book considers the current state of knowledge in all the aspects of the subject. The editors start with introductory chapters on low-dimensional topology, covering both the geometric and algebraic sides of the subject, the latter including crossed modules, Reidemeister-Peiffer identities, and a concrete and modern discussion of Whitehead's algebraic classification of 2-dimensional homotopy types. Further chapters have been skilfully selected and woven together to form a coherent picture. The latest algebraic results and their applications to 3- and 4-dimensional manifolds are dealt with. The geometric nature of the subject is illustrated to the full by over 100 diagrams. Final chapters summarize and contribute to the present status of the conjectures of Zeeman, Whitehead, and Andrews-Curtis. No other book covers all these topics. Some of the material here has been used in courses, making this book valuable for anyone with an interest in two-dimensional homotopy theory, from graduate students to research workers. 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 Homotopy theory. http://id.loc.gov/authorities/subjects/sh85061803 Combinatorial group theory. http://id.loc.gov/authorities/subjects/sh85028806 Low-dimensional topology. http://id.loc.gov/authorities/subjects/sh85078631 Homotopie. Théorie combinatoire des groupes. Topologie de basse dimension. MATHEMATICS Topology. bisacsh Combinatorial group theory fast Homotopy theory fast Low-dimensional topology fast Kombinatorische Gruppentheorie gnd http://d-nb.info/gnd/4219556-1 Homotopiemannigfaltigkeit gnd http://d-nb.info/gnd/4160627-9 Homotopie. gtt Homotopie. ram Groupes combinatoires, théorie des. ram Topologie de basse dimension. ram Algebraic topology Hog-Angeloni, Cynthia. Metzler, W. (Wolfgang) https://id.oclc.org/worldcat/entity/E39PCjvWvjq3dpCkCD4vyQHtDm http://id.loc.gov/authorities/names/n88208203 Sieradski, Allan J. Print version: Two-dimensional homotopy and combinatorial group theory. Cambridge ; New York, NY : Cambridge University Press, 1993 0521447003 (DLC) 94176225 (OCoLC)29633587 London Mathematical Society lecture note series ; 197. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552497 Volltext |
| spellingShingle | Two-dimensional homotopy and combinatorial group theory / London Mathematical Society lecture note series ; 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 Homotopy theory. http://id.loc.gov/authorities/subjects/sh85061803 Combinatorial group theory. http://id.loc.gov/authorities/subjects/sh85028806 Low-dimensional topology. http://id.loc.gov/authorities/subjects/sh85078631 Homotopie. Théorie combinatoire des groupes. Topologie de basse dimension. MATHEMATICS Topology. bisacsh Combinatorial group theory fast Homotopy theory fast Low-dimensional topology fast Kombinatorische Gruppentheorie gnd http://d-nb.info/gnd/4219556-1 Homotopiemannigfaltigkeit gnd http://d-nb.info/gnd/4160627-9 Homotopie. gtt Homotopie. ram Groupes combinatoires, théorie des. ram Topologie de basse dimension. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85061803 http://id.loc.gov/authorities/subjects/sh85028806 http://id.loc.gov/authorities/subjects/sh85078631 http://d-nb.info/gnd/4219556-1 http://d-nb.info/gnd/4160627-9 |
| title | Two-dimensional homotopy and combinatorial group theory / |
| title_auth | Two-dimensional homotopy and combinatorial group theory / |
| title_exact_search | Two-dimensional homotopy and combinatorial group theory / |
| title_full | Two-dimensional homotopy and combinatorial group theory / edited by Cynthia Hog-Angeloni, Wolfgang Metzler and Allan J. Sieradski. |
| title_fullStr | Two-dimensional homotopy and combinatorial group theory / edited by Cynthia Hog-Angeloni, Wolfgang Metzler and Allan J. Sieradski. |
| title_full_unstemmed | Two-dimensional homotopy and combinatorial group theory / edited by Cynthia Hog-Angeloni, Wolfgang Metzler and Allan J. Sieradski. |
| title_short | Two-dimensional homotopy and combinatorial group theory / |
| title_sort | two dimensional homotopy and combinatorial group theory |
| topic | Homotopy theory. http://id.loc.gov/authorities/subjects/sh85061803 Combinatorial group theory. http://id.loc.gov/authorities/subjects/sh85028806 Low-dimensional topology. http://id.loc.gov/authorities/subjects/sh85078631 Homotopie. Théorie combinatoire des groupes. Topologie de basse dimension. MATHEMATICS Topology. bisacsh Combinatorial group theory fast Homotopy theory fast Low-dimensional topology fast Kombinatorische Gruppentheorie gnd http://d-nb.info/gnd/4219556-1 Homotopiemannigfaltigkeit gnd http://d-nb.info/gnd/4160627-9 Homotopie. gtt Homotopie. ram Groupes combinatoires, théorie des. ram Topologie de basse dimension. ram |
| topic_facet | Homotopy theory. Combinatorial group theory. Low-dimensional topology. Homotopie. Théorie combinatoire des groupes. Topologie de basse dimension. MATHEMATICS Topology. Combinatorial group theory Homotopy theory Low-dimensional topology Kombinatorische Gruppentheorie Homotopiemannigfaltigkeit Groupes combinatoires, théorie des. |
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