Two-Dimensional Homotopy and Combinatorial Group TheoryCynthia Hog-Angeloni, Wolfgang Metzler, Allan J. Sieradski Cambridge University Press, 9 дек. 1993 г. - Всего страниц: 412 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. |
Содержание
I Geometric Aspects of TwoDimensional Complexes | 1 |
II Algebraic Topology for Two Dimensional Complexes | 51 |
III Homotopy and Homology Classification of 2Complexes | 97 |
IV Crossed Modules and n2 Homotopy Modules | 125 |
V Calculating Generators of n2 | 157 |
VI Applications of Diagrams to Decision Problems | 189 |
VII Fox Ideals NTorsion and Applications to Groups and 3Manifolds | 219 |
VIII Singular 3Manifolds | 251 |
IX Cancellation Results for 2Complexes and 4Manifolds and Some Applications | 281 |
X J H C Whiteheads Asphericity Question | 309 |
XI Zeemans Collapsing Conjecture | 335 |
XII The AndrewsCurtis Conjecture and its Generalizations | 365 |
Bibliography | 381 |
| 408 | |
Часто встречающиеся слова и выражения
1-skeleton 2-cells 2-dimensional 3-deformation 3-manifold abelian group algebraic aspherical aspherical 2-complex attaching maps basepoint boundary cells cellular chain complex chain map Chapter Cockcroft collapse combinatorial connected 2-complex connected subcomplex corresponding crossed modules CW-complex cycles cyclic defined denote diagram dimension disc edge element embedded equivariant Euler characteristic example Figure finite group finite presentation free group free product fundamental group G-crossed graph group G H₁(N Heegaard splitting hence homology homomorphism homotopy class homotopy equivalence homotopy groups homotopy type hyperbolic identity implies induced inverse isomorphism J. H. C. Whitehead Lemma manifold Math normal pair polyhedra polyhedron quotient regular neighbourhood relator resp result sequence simple-homotopy equivalent simplicial special polyhedron spherical picture spine subgroup theory thickening topological trivial universal covering vertex vertices w₁ Whitehead ZG-module