Skip to main content
SpringerLink
Log in

Surgery on Simply-Connected Manifolds

  • Book
  • © 1972

Overview

Authors:
  1. William Browder

    1. Princeton University, Princeton, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge (MATHE2, volume 65)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (5 chapters)

  1. Front Matter

    Pages I-IX
    Download chapter PDF

  2. Poincaré Duality

    • William Browder
    Pages 1-29

  3. The Main Results of Surgery

    • William Browder
    Pages 30-50

  4. The Invariant σ

    • William Browder
    Pages 51-82

  5. Surgery and the Fundamental Theorem

    • William Browder
    Pages 83-113

  6. Plumbing

    • William Browder
    Pages 114-126

  7. Back Matter

    Pages 127-134
    Download chapter PDF
Back to top

Keywords

About this book

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.

Authors and Affiliations

  • Princeton University, Princeton, USA

    William Browder

Bibliographic Information

  • Book Title: Surgery on Simply-Connected Manifolds

  • Authors: William Browder

  • Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge

  • DOI: https://doi.org/10.1007/978-3-642-50020-6

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1972

  • Softcover ISBN: 978-3-642-50022-0Published: 07 July 2012

  • eBook ISBN: 978-3-642-50020-6Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: X, 134

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Topology

Publish with us

Policies and ethics

Back to top

Search

Navigation