Homotopy Type and Homology [Hardcover]

The author, a leading figure in algebraic topology, provides a modern treatment of a long established set of questions in this important research area. The book's principal objective--and main result--is the classification theorem onk-variants and boundary invariants, which supplement the classical picture of homology and homotopy groups, along with computations of types that are obtained by applying this theorem. Research mathematicians in algebraic topology will be interested in this new attempt to classify homotopy types of simply connected CW-complexes.

Introduction
1. Linear extension and Moore spaces
2. Invariants of homotopy types
3. On the classification of homotopy types
4. The CW-tower of categories
5. Spaniert-Whitehead duality and the stable CW-tower
6. Eilenberg-Mac Lane functors
7. Moore functors
8. The homotopy category of (n-1)-connected (n+1)-types
8. On the homotopy classification of (n-1)-connected (n+3)-dimensional polyhedra,n>4
9. On the homotopy classification of 2-connected 6-dimensional polyhedra
10. Decomposition of homotopy types
11. Homotopy groups in dimension 4
12. On the homotopy classification of simply connected 5-dimensional polyhedra
13. Primary homotopy operations and homotopy groups of mapping cones
Bibliography
Index