Diffeomorphisms of elliptic 3-manifolds

著者

• Hong, Sungbok

書誌事項

Diffeomorphisms of elliptic 3-manifolds

Sungbok Hong ... [et al.]

（Lecture notes in mathematics, 2055）

Springer, c2012

注記

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

内容説明・目次

内容説明

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

目次

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

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詳細情報

• NII書誌ID(NCID): BB10250082
• ISBN:
  • 9783642315633
• LCCN: 2012945525
• 出版国コード: gw
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Berlin
• ページ数/冊数: x, 155 p.
• 大きさ: 24 cm
• 分類:
  • SG : 510
• 親書誌ID:
  • BA00146586