The Homotopy Category of Simply Connected 4-Manifolds
London Mathematical Society Lecture Note Series

The homotopy type of a closed simply connected 4-manifold is determined by the intersection form. The homotopy classes of maps between two such manifolds, however, do not coincide with the algebraic morphisms between intersection forms. Therefore the problem arises of computing the homotopy classes of maps algebraically and determining the law of composition for such maps. This problem is solved in the book by introducing new algebraic models of a 4-manifold. The book has been written to appeal to both established researchers in the field and graduate students interested in topology and algebra. There are many references to the literature for those interested in further reading.

Introduction; 1. The homotopy category of (2,4)-complexes; 2. The homotopy category of simply connected 4-manifolds; 3. Track categories; 4. The splitting of the linear extension TL; 5. The category T Gamma and an algebraic model of CW(2,4); 6. Crossed chain complexes and algebraic models of tracks; 7. Quadratic chain complexes and algebraic models of tracks; 8. On the cohomology of the category nil.