The Algebraic Characterization of Geometric 4-Manifolds

By: J. A. Hillman

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Paperback | 4 April 1994

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184 Pages

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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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Non-Fiction Mathematics Geometry Differential & Riemannian Geometry Algebraic Geometry Topology Applied Mathematics

Preface
Algebraic preliminaries
General results on the homotopy type of 4-manifolds
Mapping tori and circle bundles
Surface bundles
Simple homotopy type, s-cobordism and homeomorphism
Aspherical geometries
Manifolds covered by S2 x R2
Manifolds covered by S3 x R
Geometries with compact models
Applications to 2-knots and complex surfaces
Appendix
Problems
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

The Algebraic Characterization of Geometric 4-Manifolds

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Paperback

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