The algebraic characterization of geometric 4-manifolds
Author(s)
Bibliographic Information
The algebraic characterization of geometric 4-manifolds
（London Mathematical Society lecture note series, 198）
Cambridge University Press, 1994
Available at 72 libraries
Note
Includes bibliographical references (p. 160-168) and index
Description and Table of Contents
Description
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.
Table of Contents
- 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.
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