Surgery on compact manifolds
著者
書誌事項
Surgery on compact manifolds
(Mathematical surveys and monographs, v. 69)
American Mathematical Society, c1999
2nd ed. / edited by A.A. Ranicki
大学図書館所蔵 全59件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references (p. 285-299) and index
内容説明・目次
内容説明
The publication of this book in 1970 marked the culmination of a particularly exciting period in the history of the topology of manifolds. The world of high-dimensional manifolds had been opened up to the classification methods of algebraic topology by Thom's work in 1952 on transversality and cobordism, the signature theorem of Hirzebruch in 1954, and by the discovery of exotic spheres by Milnor in 1956. In the 1960s, there had been an explosive growth of interest in the surgery method of understanding the homotopy types of manifolds (initially in the differentiable category), including results such as the $h$-cobordism theory of Smale (1960), the classification of exotic spheres by Kervaire and Milnor (1962), Browder's converse to the Hirzebruch signature theorem for the existence of a manifold in a simply connected homotopy type (1962).It also includes the $s$-cobordism theorem of Barden, Mazur, and Stallings (1964), Novikov's proof of the topological invariance of the rational Pontrjagin classes of differentiable manifolds (1965), the fibering theorems of Browder and Levine (1966) and Farrell (1967), Sullivan's exact sequence for the set of manifold structures within a simply connected homotopy type (1966), Casson and Sullivan's disproof of the Hauptvermutung for piecewise linear manifolds (1967), Wall's classification of homotopy tori (1969), and Kirby and Siebenmann's classification theory of topological manifolds (1970). The original edition of the book fulfilled five purposes by providing: a coherent framework for relating the homotopy theory of manifolds to the algebraic theory of quadratic forms, unifying many of the previous results; a surgery obstruction theory for manifolds with arbitrary fundamental group, including the exact sequence for the set of manifold structures within a homotopy type, and many computations; the extension of surgery theory from the differentiable and piecewise linear categories to the topological category; a survey of most of the activity in surgery up to 1970; and, a setting for the subsequent development and applications of the surgery classification of manifolds. This new edition of this classic book is supplemented by notes on subsequent developments. References have been updated and numerous commentaries have been added. The volume remains the single most important book on surgery theory.
目次
- Preliminaries: Note on conventions Basic homotopy notions Surgery below the middle dimension Appendix: Applications Simple Poincare complexes The main theorem: Statement of results An important special case The even-dimensional case The odd-dimensional case The bounded odd-dimensional case The bounded even-dimensional case Completion of the proof Patterns of application: Manifold structures on Poincare complexes Applications to submanifolds Submanifolds: Other techniques Separating submanifolds Two-sided submanifolds One-sided submanifolds Calculations and applications: Calculations: Surgery obstruction groups Calculations: The surgery obstructions Applications: Free actions on spheres
- General remarks An extension of the Atiyah-Singer $G$-signature theorem Free actions of $S^1$ Fake projective spaces (real) Fake lens spaces Applications: Free uniform actions on euclidean space Fake tori Polycyclic groups Applications to 4-manifolds Postscript: Further ideas and suggestions: Recent work
- Function space methods Topological manifolds Poincare embeddings Homotopy and simple homotopy Further calculations Sullivan's results Reformulations of the algebra Rational surgery References Index.
「Nielsen BookData」 より