The Algebraic Characterization of Geometric 4-Manifolds [Paperback]

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