Springer Monographs in Mathematics

The Geometric Hopf Invariant and Surgery Theory

Authors: Crabb, Michael, Ranicki, Andrew

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  • Provides the homotopy theoretic foundations for surgery theory
  • Includes a self-contained account of the Hopf invariant in terms of Z_2-equivariant homotopy
  • Covers applications of the Hopf invariant to surgery theory, in particular the Double Point Theorem
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eBook 71,68 €
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  • ISBN 978-3-319-71306-9
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Hardcover 124,79 €
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  • ISBN 978-3-319-71305-2
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Softcover 88,39 €
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  • ISBN 978-3-319-89061-6
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About this book

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. 

Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook 71,68 €
price for Spain (gross)
  • ISBN 978-3-319-71306-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 124,79 €
price for Spain (gross)
  • ISBN 978-3-319-71305-2
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 88,39 €
price for Spain (gross)
  • ISBN 978-3-319-89061-6
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
The Geometric Hopf Invariant and Surgery Theory
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-71306-9
DOI
10.1007/978-3-319-71306-9
Hardcover ISBN
978-3-319-71305-2
Softcover ISBN
978-3-319-89061-6
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XVI, 397
Number of Illustrations
1 illustrations in colour
Topics