The algebraic characterization of geometric 4-manifolds

Bibliographic Information

The algebraic characterization of geometric 4-manifolds

J.A. Hillman

(London Mathematical Society lecture note series, 198)

Cambridge University Press, 1994

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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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Details

  • NCID
    BA21777348
  • ISBN
    • 0521467780
  • Country Code
    uk
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Cambridge
  • Pages/Volumes
    ix, 170 p.
  • Size
    23 cm
  • Classification
  • Parent Bibliography ID
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