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Springer Monographs in Mathematics

Fibrewise Homotopy Theory

Authors: Crabb, Michael Charles, James, Ioan Mackenzie

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  • Ioan James is an Internationally well-known expert in this field and an experienced author * Fibrewise Homotopy Theory is a very large subject that has attracted a good deal of research in recent years * The authors provide an overview of fibrewise homotopy theory as it stands at present; a kind of expository survey * Ioan James has been interested in this subject for a number of years, and in addition to the expository text, a good deal of the material is completely new * The main advantage of this monograph is that one does not have to be an expert in classical stable theory to understand and enjoy it

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About this book

Topology occupies a central position in the mathematics of today. One of the most useful ideas to be introduced in the past sixty years is the concept of fibre bundle, which provides an appropriate framework for studying differential geometry and much else. Fibre bundles are examples of the kind of structures studied in fibrewise topology. Just as homotopy theory arises from topology, so fibrewise homotopy theĀ­ ory arises from fibrewise topology. In this monograph we provide an overview of fibrewise homotopy theory as it stands at present. It is hoped that this may stimulate further research. The literature on the subject is already quite extensive but clearly there is a great deal more to be done. Efforts have been made to develop general theories of which ordinary homotopy theory, equivariant homotopy theory, fibrewise homotopy theory and so forth will be special cases. For example, Baues [7] and, more recently, Dwyer and Spalinski [53], have presented such general theories, derived from an earlier theory of Quillen, but none of these seem to provide quite the right framework for our purposes. We have preferred, in this monograph, to develop fibre wise homotopy theory more or less ab initio, assuming only a basic knowledge of ordinary homotopy theory, at least in the early sections, but our aim has been to keep the exposition reasonably self-contained.

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $69.99
price for USA in USD (gross)
  • ISBN 978-1-4471-1265-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA in USD
  • ISBN 978-1-4471-1267-9
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Fibrewise Homotopy Theory
Authors
Series Title
Springer Monographs in Mathematics
Copyright
1998
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London Limited
eBook ISBN
978-1-4471-1265-5
DOI
10.1007/978-1-4471-1265-5
Softcover ISBN
978-1-4471-1267-9
Series ISSN
1439-7382
Edition Number
1
Number of Pages
VIII, 341
Topics

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