The Algebraic Characterization of Geometric 4-Manifolds
The Algebraic Characterization of Geometric 4-Manifolds
J. A. Hillman, University of Sydney
February 2011
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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.
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February 2011Adobe eBook Reader
9780511892936
0 pages
0kg
This ISBN is for an eBook version which is distributed on our behalf by a third party.
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.
