The homotopy category of simply connected 4-manifolds / Hans Joachim Baues.

Format:

Book

Author/Creator:

Baues, Hans J., 1943- author.

Contributor:

London Mathematical Society, issuing body.

Series:

London Mathematical Society lecture note series ; 297.

London Mathematical Society lecture note series ; 297

Language:

English

Subjects (All):

Homotopy theory.

Four-manifolds (Topology).

Physical Description:

1 online resource (xi, 184 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2003.

Language Note:

English

Summary:

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.

Contents:

1. homotopy category of (2,4)-complexes

2. homotopy category of simply connected 4-manifolds

3. Track categories

4. splitting of the linear extension TL

5. 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. (T. Pirashvili).

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. [179]-181) and index.

ISBN:

1-139-88209-0

1-107-08889-5

1-107-09178-0

1-107-10070-4

1-107-09505-0

1-107-10325-8

1-107-32589-7