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Surgery on Simply-Connected Manifolds

  • William Browder

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 65)

Table of contents

  1. Front Matter
    Pages I-IX
  2. William Browder
    Pages 1-29
  3. William Browder
    Pages 30-50
  4. William Browder
    Pages 51-82
  5. William Browder
    Pages 83-113
  6. William Browder
    Pages 114-126
  7. Back Matter
    Pages 127-134

About this book

Introduction

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.

Keywords

Invariant Manifolds Mannigfaltigkeit character differentiable manifold duality form homotopy manifold proof proving theorem

Authors and affiliations

  • William Browder
    • 1
  1. 1.Princeton UniversityPrincetonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-50020-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 1972
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-50022-0
  • Online ISBN 978-3-642-50020-6
  • Series Print ISSN 0071-1136
  • Buy this book on publisher's site