Diffeomorphisms of elliptic 3-manifolds

Author(s)

    • Hong, Sungbok

Bibliographic Information

Diffeomorphisms of elliptic 3-manifolds

Sungbok Hong ... [et al.]

(Lecture notes in mathematics, 2055)

Springer, c2012

Available at  / 49 libraries

Search this Book/Journal

Note

Includes bibliographical references (p. 145-147) and index

Description and Table of Contents

Description

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

Table of Contents

1 Elliptic 3-manifolds and the Smale Conjecture.- 2 Diffeomorphisms and Embeddings of Manifolds.- 3 The Method of Cerf and Palais.- 4 Elliptic 3-manifolds Containing One-sided Klein Bottles.- 5 Lens Spaces

by "Nielsen BookData"

Related Books: 1-1 of 1

Details

  • NCID
    BB10250082
  • ISBN
    • 9783642315633
  • LCCN
    2012945525
  • Country Code
    gw
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Berlin
  • Pages/Volumes
    x, 155 p.
  • Size
    24 cm
  • Classification
  • Parent Bibliography ID
Page Top