Combinatorial Homotopy and 4-Dimensional Complexes / / Hans-Joachim Baues.

• Superior document: Title is part of eBook package: De Gruyter DG Expositions in Mathematics Backlist eBook Package
• VerfasserIn: Baues, Hans-Joachim,
• MitwirkendeR: Brown, Ronald,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2011]; ©1991
• Year of Publication: 2011
• Edition: Reprint 2011
• Language: English
• Series: De Gruyter Expositions in Mathematics , 2
• Physical Description: 1 online resource (380 p.)

Table of Contents

Frontmatter -- Chapter I. Homotopy, homology, and Whitehead’s classification of simply connected 4-dimensional CW-complexes -- Chapter II. The CW-tower of categories -- Chapter III. Crossed modules and homotopy systems of order 3 -- Chapter IV. Quadratic modules and homotopy systems of order 4. § 1 Quadratic modules -- Chapter IV. Quadratic modules and homotopy systems of order 4. § 2 Free quadratic modules -- Chapter IV. Quadratic modules and homotopy systems of order 4. § 3 Quadratic chain complexes -- Chapter IV. Quadratic modules and homotopy systems of order 4. § 4 Homotopies for quadratic chain maps -- Chapter IV. Quadratic modules and homotopy systems of order 4. § 5 Cofibrations in the category of quadratic chain complexes -- Chapter IV. Quadratic modules and homotopy systems of order 4. § 6 The secondary homotopy addition lemma and a model functor from spaces to quadratic chain complexes -- Chapter IV. Quadratic modules and homotopy systems of order 4. § 7 Homotopy systems of order 4 -- Chapter IV. Quadratic modules and homotopy systems of order 4. § 8 The homotopy category of 3-dimensional CW-complexes -- Chapter IV. Quadratic modules and homotopy systems of order 4. § 9 The CW-tower in degree ≤ 4 -- Chapter IV. Quadratic modules and homotopy systems of order 4. § 10 The homotopy category of 3-types -- Chapter IV. Quadratic modules and homotopy systems of order 4. § 11 The action of the fundamental group for quadratic chain complexes -- Chapter IV. Quadratic modules and homotopy systems of order 4. § 12 The quadratic chain complex of a product -- Chapter IV. Quadratic modules and homotopy systems of order 4. Appendix A. Some diverse examples and applications of quadratic chain complexes -- Chapter IV. Quadratic modules and homotopy systems of order 4. Appendix B. Quadratic chain complexes and simplicial groups -- Chapter IV. Quadratic modules and homotopy systems of order 4. Appendix C. Reduced and stable quadratic modules -- Chapter IV. Quadratic modules and homotopy systems of order 4. Appendix D. On the homotopy classification of semi free group actions -- Chapter V. Cohomological invariants -- Chapter VI. The cohomology of categories and the calculus of tracks -- Bibliography -- List of Symbols -- Index