Combinatorial Homotopy and 4-Dimensional Complexes

This book by Baues handles the classification of 4-dimensional complexes. Henry Whitehead commented in his famous paper, *Combinatorial homotopy I*, (1949), ‘What has been achieved so far is a purely algebraic description of the homotopy type of any 3-dimensional complex and of any finite, simply connected 4-dimensional complex.’ (This case of simply connected 4-dimensional complexes had been treated by him in another paper in that same year of 1949.) This book by Baues gives a solution in the non-simply connected case.

- Combinatorial Homotopy and 4-Dimensional Complexes.
- Contents
- Preface by Ronnie Brown.
- Introduction
- I Homotopy, homology, and Whitehead’s classification of simply connected 4-dimensional CW-complexes.
- II The CW-tower of categories
- III Crossed modules and homotopy systems of order 3
- IV Quadratic modules and homotopy systems of order 4
- V Cohomological invariants
- VI The cohomology of categories and the calculus of tracks
- Bibliography
- List of Symbols
- Index

- References

- H.-J. Baues, Combinatorial Homotopy and 4-Dimensional Complexes , de Gruyter Expositions in Mathematics 2, Walter de Gruyter, (1991).

category: reference

Revised on December 12, 2010 18:11:19
by Tim Porter
(95.147.236.70)