The Algebraic Characterization of Geometric 4-Manifolds

This book is essential reading for anyone interested in low-dimensional topology.

J. A. Hillman (Author)

9780521467780, Cambridge University Press

Paperback, published 3 February 1994

184 pages
22.8 x 15.2 x 1 cm, 0.266 kg

This book describes work, largely that of the author, on the characterization of closed 4-manifolds in terms of familiar invariants such as Euler characteristic, fundamental group, and Stiefel–Whitney classes. Using techniques from homological group theory, the theory of 3-manifolds and topological surgery, infrasolvmanifolds are characterized up to homeomorphism, and surface bundles are characterized up to simple homotopy equivalence. Non-orientable cases are also considered wherever possible, and in the final chapter the results obtained earlier are applied to 2-knots and complex analytic surfaces. This book is essential reading for anyone interested in low-dimensional topology.

Preface
1. Algebraic preliminaries
2. General results on the homotopy type of 4-manifolds
3. Mapping tori and circle bundles
4. Surface bundles
5. Simple homotopy type, s-cobordism and homeomorphism
6. Aspherical geometries
7. Manifolds covered by S2 x R2
8. Manifolds covered by S3 x R
9. Geometries with compact models
10. Applications to 2-knots and complex surfaces
Appendix
Problems
References
Index.

Subject Areas: Algebraic geometry [PBMW]