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＜電子ブック＞
Surgery on Simply-Connected Manifolds / by William Browder
(Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, A Series of Modern Surveys in Mathematics ; 65)

版	1st ed. 1972.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1972
本文言語	英語
大きさ	X, 134 p. 1 illus : online resource
著者標目	*Browder, William author SpringerLink (Online service)
件　名	LCSH:Topology FREE:Topology
一般注記	I. Poincaré Duality -- § 1. Slant Operations, Cup and Cap Products -- § 2. Poincaré Duality -- §3. Poincaré Pairs and Triads; Sums of Poincaré Pairs and Maps -- §4. The Spivak Normal Fibre Space -- II. The Main Results of Surgery -- §1. The Main Technical Results -- § 2. Transversality and Normal Cobordism -- § 3. Homotopy Types of Smooth Manifolds and Classification -- § 4. Reinterpretation Using the Spivak Normal Fibre Space -- III. The Invariant ? -- § 1. Quadratic Forms over ? and ?2 -- §2. The Invariant I(f), (index) -- § 3. Normal Maps, Wu Classes, and the Definition of ? for m = 4l -- § 4. The Invariant c(f, b) (Kervaire invariant) -- § 5. Product Formulas -- IV. Surgery and the Fundamental Theorem -- § 1. Elementary Surgery and the Group SO(n) -- §2. The Fundamental Theorem: Preliminaries -- §3. Proof of the Fundamental Theorem for m odd -- § 4. Proof of the Fundamental Theorem for m even -- V. Plumbing -- § 1. Intersection -- §2. Plumbing Disk Bundles This book is an exposition of the technique of surgery on simply-connected smooth manifolds. Systematic study of differentiable manifolds using these ideas was begun by Milnor [45] and Wallace [68] and developed extensively in the last ten years. It is now possible to give a reasonably complete theory of simply-connected manifolds of dimension ~ 5 using this approach and that is what I will try to begin here. The emphasis has been placed on stating and proving the general results necessary to apply this method in various contexts. In Chapter II, these results are stated, and then applications are given to characterizing the homotopy type of differentiable manifolds and classifying manifolds within a given homotopy type. This theory was first extensively developed in Kervaire and Milnor [34] in the case of homotopy spheres, globalized by S. P. Novikov [49] and the author [6] for closed 1-connected manifolds, and extended to the bounded case by Wall [65] and Golo [23]. The thesis of Sullivan [62] reformed the theory in an elegant way in terms of classifying spaces HTTP:URL=https://doi.org/10.1007/978-3-642-50020-6

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