Combinatorial Homotopy and 4-Dimensional Complexes
Synthesis, Screening and Application Potential
1st Edition
Published on 12. May 2011
XXVII, 380 pages
978-3-11-085448-0 (ISBN)
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"This is an impressive and substantial book containing significant new ideas in a rather unfashionable area." Mathematical Reviews
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Hans-Joachim Baues
Combinatorial Homotopy and 4-Dimensional Complexes
Book
01/1991
1st Edition
De Gruyter
€239.00
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Hans-Joachim Baues
Combinatorial Homotopy and 4-Dimensional Complexes
Book
01/1991
1st Edition
De Gruyter
€169.95
Shipment within 7-9 days
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Content
- Intro
- 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 G 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
- § 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
- §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 planes
- Chapter 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
- § 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 The classification of special 4-dimensional homotopy types by Pontrjagin squares
- § 5 Natural quotients of the Postnikov chain functor
- § 6 Pontrjagin squares with local coefficients
- Appendix A. The stable equivalence classes of finite 4-dimensional complexes
- Chapter VI. The cohomology of categories and the calculus of tracks
- § 1 The cohomology of categories
- § 2 The category of free nil(2)-groups and the existence of Pontrjagin squares
- § 3 Linear track extensions of categories
- § 4 Free nil(2)-groups and tracks for one point unions of n-spheres
- § 5 Tracks for one point unions of n-spheres with operators in groups
- § 6 Free nil(2)-modules and tracks for 2-dimensional CW-complexes
- § 7 Track-models for 4-dimensional CW-complexes
- Bibliography
- List of Symbols
- Index
