Diffeomorphisms of Elliptic 3-Manifolds

  • Sungbok Hong
  • John Kalliongis
  • Darryl McCullough
  • J. Hyam Rubinstein
Part of the Lecture Notes in Mathematics book series (LNM, volume 2055)

Table of contents

  1. Front Matter
    Pages i-x
  2. Sungbok Hong, John Kalliongis, Darryl McCullough, J. Hyam Rubinstein
    Pages 1-7
  3. Sungbok Hong, John Kalliongis, Darryl McCullough, J. Hyam Rubinstein
    Pages 9-17
  4. Sungbok Hong, John Kalliongis, Darryl McCullough, J. Hyam Rubinstein
    Pages 19-51
  5. Sungbok Hong, John Kalliongis, Darryl McCullough, J. Hyam Rubinstein
    Pages 53-83
  6. Sungbok Hong, John Kalliongis, Darryl McCullough, J. Hyam Rubinstein
    Pages 85-144
  7. Back Matter
    Pages 145-155

About this book

Introduction

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 material on diffeomorphism groups is included.

Keywords

3-manifold 57M99, 57S10, 58D05, 58D29 Frechet Smale Conjecture elliptic

Authors and affiliations

  • Sungbok Hong
    • 1
  • John Kalliongis
    • 2
  • Darryl McCullough
    • 3
  • J. Hyam Rubinstein
    • 4
  1. 1.Department of MathematicsKorea UniversitySeoulKorea, Republic of (South Korea)
  2. 2.Dept. of Mathematics & Computer ScienceSaint Louis UniversitySt. LouisUSA
  3. 3.Department of MathematicsUniversity of OklahomaNormanUSA
  4. 4.Department of MathematicsUniversity of MelbourneMelbourneAustralia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-31564-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 2012
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-31563-3
  • Online ISBN 978-3-642-31564-0
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book