UID:
almahu_9947360002402882
Format:
Online-Ressource (xxvii, 380 p)
,
ill
Edition:
Online-Ausg. Palo Alto, Calif ebrary 2011 Electronic reproduction; Available via World Wide Web
ISBN:
089925697X (acid-free)
,
3110124882 (acid-free)
,
9783110124880 (acid-free)
Series Statement:
De Gruyter expositions in mathematics 2
Content:
Combinatorial Homotopy and 4-Dimensional Complexes (Architektur Auf Naxos Und Paros)
Note:
Includes bibliographical references (p. [369]-372) and index
,
1 Linear extensions of categories and exact sequences for functors 2 Homotopy systems of order (n + 1); 3 The CW-tower of categories; 4 The Postnikov chain functor; 5 Three formulas for the obstruction; 6 Trees of homotopy types; 7 On the homotopy classification of manifolds with finite fundamental group; Chapter III. Crossed modules and homotopy systems of order 3; 1 Nilpotent groups and Peiffer nilpotent pre-crossed modules; 2 Crossed chain complexes and homotopy systems of order 3; 3 Cylinders of CW-complexes and of crossed chain complexes.
,
11 The action of the fundamental group for quadratic chain complexes 12 The quadratic chain complex of a product; Appendix A. Some diverse examples and applications of quadratic chain complexes; Appendix B. Quadratic chain complexes and simplicial groups; Appendix C. Reduced and stable quadratic modules; Appendix D. On the homotopy classification of semi free group actions; Chapter V. Cohomological invariants; 1 The classification of 4-dimensional homotopy types; 2 A new cohomological invariant and the cup product.
,
3 Obstructions for the existence of certain chain maps and the primary obstruction for the realizability of a chain complex.
,
4 Cofibrations in the category of crossed chain complexes 5 The homotopy addition lemma; 6 A model functor from spaces to crossed chain complexes; 7 The homotopy category of 2-dimensional CW-complexes; 8 The homotopy category of 2-types; 9 The crossed chain complex of a product; 10 The action of the fundamental group and free homotopy classes; Appendix A. Obstructions for the realizability of chain complexes; Appendix B. The homotopy category of pseudo projective planes; Appendix C. On the suspension and the James construction.
,
Appendix D. The homotopy category of suspended pseudo projective planesChapter IV. Quadratic modules and homotopy systems of order 4; 1 Quadratic modules; 2 Free quadratic modules; 3 Quadratic chain complexes; 4 Homotopies for quadratic chain maps; 5 Cofibrations in the category of quadratic chain complexes; 6 The secondary homotopy addition lemma and a model functor from spaces to quadratic chain complexes; 7 Homotopy systems of order 4; 8 The homotopy category of 3-dimensional CW-complexes; 9 The CW-tower in degree ≤ 4; 10 The homotopy category of 3-types.
,
Preface by Ronald Brown; Introduction; Chapter I. Homotopy, homology, and Whitehead's classification of simply connected 4-dimensional CW-complexes; 0 Sufficiency, realizability and detecting functors; 1 Homotopy groups; 2 CW-complexes and homology with local coefficients; 3 Whitehead's certain exact sequence; 4 The quadratic functor Γ and central extensions; 5 Cup products and Pontrjagin squares; 6 Cohomological invariants; 7 An2-polyhedra and An2-forms; 8 Whitehead's classification of An2-polyhedra, n ≥ 2; Chapter II. The CW-tower of categories.
Additional Edition:
ISBN 9783110854480
Language:
English
DOI:
10.1515/9783110854480
URL:
http://www.degruyter.com/doi/book/10.1515/9783110854480
