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The Geometric Hopf Invariant and Surgery Theory

  • Michael Crabb
  • Andrew Ranicki

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Michael Crabb, Andrew Ranicki
    Pages 1-15
  3. Michael Crabb, Andrew Ranicki
    Pages 17-38
  4. Michael Crabb, Andrew Ranicki
    Pages 39-75
  5. Michael Crabb, Andrew Ranicki
    Pages 127-208
  6. Michael Crabb, Andrew Ranicki
    Pages 209-295
  7. Michael Crabb, Andrew Ranicki
    Pages 297-304
  8. Michael Crabb, Andrew Ranicki
    Pages 305-327
  9. Back Matter
    Pages 329-397

About this book

Introduction

Written by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional manifolds.

Presenting classical ideas in a modern framework, the authors carefully highlight how their results relate to (and generalize) existing results in the literature. The central result of the book expresses algebraic surgery theory in terms of the geometric Hopf invariant, a construction in stable homotopy theory which captures the double points of immersions. Many illustrative examples and applications of the abstract results are included in the book, making it of wide interest to topologists.

Serving as a valuable reference, this work is aimed at graduate students and researchers interested in understanding how the algebraic and geometric topology fit together in the surgery theory of manifolds. It is the only book providing such a wide-ranging historical approach to the Hopf invariant, double points and surgery theory, with many results old and new. 

Keywords

MSC (2010): 55Q25, 57R42 geometric Hopf invariant manifolds doube points of maps double point theorem algebraic surgery difference construction homotopy difference construction chain homotopy coordinate-free approach to stable homotopy theory inner product spaces stable homotopy theory Z_2 equivariant homotopy bordism theory surgery obstruction theory

Authors and affiliations

  • Michael Crabb
    • 1
  • Andrew Ranicki
    • 2
  1. 1.Institute of MathematicsUniversity of AberdeenAberdeenUnited Kingdom
  2. 2.School of MathematicsUniversity of EdinburghEdinburghUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-71306-9
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-71305-2
  • Online ISBN 978-3-319-71306-9
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • Buy this book on publisher's site