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Book Cover
PRINTED BOOKS
Author Hillman, Jonathan A. (Jonathan Arthur), 1947-

Title The algebraic characterization of geometric 4-manifolds / J.A. Hillman.

Published Cambridge : Cambridge University Press, 1994.

Copies

Location Call No. Status
 UniM ERC  514.34 HILL    AVAILABLE
Physical description ix, 170 pages ; 23 cm.
Series London Mathematical Society lecture note series ; 198.
London Mathematical Society lecture note series ; 198.
Bibliography Includes bibliographical reference (pages 160-168) and index.
Contents I. Algebraic Preliminaries -- II. General results on the homotopy type of 4-manifolds -- III. Mapping tori and circle bundles -- IV. Surface bundles -- V. Simple homotopy type, s-cobordism and homeomorphism -- VI. Aspherical geometries -- VII. Manifolds covered by S[superscript 2] x R[superscript 2] -- VIII. Manifolds covered by S[superscript 3] x R -- IX. Geometries with compact models -- x. Applications to 2-knots and complex surfaces -- Appendix 3-dimensional Poincare duality complexes.
Summary 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.
Subject Four-manifolds (Topology)
Homotopy theory.
Algebraic topology.
ISBN 0521467780