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Diffeomorphisms of Elliptic 3-Manifolds

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  • © 2012

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Authors:
  1. Sungbok Hong

    1. Department of Mathematics, Korea University, Seoul, Korea, Republic of (South Korea)

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  2. John Kalliongis

    1. Dept. of Mathematics & Computer Science, Saint Louis University, St. Louis, USA

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  3. Darryl McCullough

    1. Department of Mathematics, University of Oklahoma, Norman, USA

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  4. J. Hyam Rubinstein

    1. Department of Mathematics, University of Melbourne, Melbourne, Australia

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 2055)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-x
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  2. Elliptic Three-Manifolds and the Smale Conjecture

    • Sungbok Hong, John Kalliongis, Darryl McCullough, J. Hyam Rubinstein
    Pages 1-7

  3. Diffeomorphisms and Embeddings of Manifolds

    • Sungbok Hong, John Kalliongis, Darryl McCullough, J. Hyam Rubinstein
    Pages 9-17

  4. The Method of Cerf and Palais

    • Sungbok Hong, John Kalliongis, Darryl McCullough, J. Hyam Rubinstein
    Pages 19-51

  5. Elliptic Three-Manifolds Containing One-Sided Klein Bottles

    • Sungbok Hong, John Kalliongis, Darryl McCullough, J. Hyam Rubinstein
    Pages 53-83

  6. Lens Spaces

    • Sungbok Hong, John Kalliongis, Darryl McCullough, J. Hyam Rubinstein
    Pages 85-144

  7. Back Matter

    Pages 145-155
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Keywords

About this book

This work concerns the diffeomorphism groups of 3-manifolds, in particular of elliptic 3-manifolds. These are the closed 3-manifolds that admit a Riemannian metric of constant positive curvature, now known to be exactly the closed 3-manifolds that have a finite fundamental group. The (Generalized) Smale Conjecture asserts that for any elliptic 3-manifold M, the inclusion from the isometry group of M to its diffeomorphism group is a homotopy equivalence. The original Smale Conjecture, for the 3-sphere, was proven by J. Cerf and A. Hatcher, and N. Ivanov proved the generalized conjecture for many of the elliptic 3-manifolds that contain a geometrically incompressible Klein bottle.

The main results establish the Smale Conjecture for all elliptic 3-manifolds containing geometrically incompressible Klein bottles, and for all lens spaces L(m,q) with m at least 3. Additional results imply that for a Haken Seifert-fibered 3 manifold V, the space of Seifert fiberings has contractible components, and apart from a small list of known exceptions, is contractible. Considerable foundational and background

Authors and Affiliations

  • Department of Mathematics, Korea University, Seoul, Korea, Republic of (South Korea)

    Sungbok Hong

  • Dept. of Mathematics & Computer Science, Saint Louis University, St. Louis, USA

    John Kalliongis

  • Department of Mathematics, University of Oklahoma, Norman, USA

    Darryl McCullough

  • Department of Mathematics, University of Melbourne, Melbourne, Australia

    J. Hyam Rubinstein

Bibliographic Information

  • Book Title: Diffeomorphisms of Elliptic 3-Manifolds

  • Authors: Sungbok Hong, John Kalliongis, Darryl McCullough, J. Hyam Rubinstein

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-31564-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2012

  • Softcover ISBN: 978-3-642-31563-3Published: 28 August 2012

  • eBook ISBN: 978-3-642-31564-0Published: 29 August 2012

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 155

  • Number of Illustrations: 22 b/w illustrations

  • Topics: Manifolds and Cell Complexes (incl. Diff.Topology)

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