Surveys on Surgery Theory: Volume 1. Papers Dedicated to C. T. C. Wall. (AM-145)

Overview

Surgery theory, the basis for the classification theory of manifolds, is now about forty years old. There have been some extraordinary accomplishments in that time, which have led to enormously varied interactions with algebra, analysis, and geometry. Workers in many of these areas have often lamented the lack of a single source that surveys surgery theory and its applications. Indeed, no one person could write such a survey.

The sixtieth birthday of C. T. C. Wall, one of the ...

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Overview

Surgery theory, the basis for the classification theory of manifolds, is now about forty years old. There have been some extraordinary accomplishments in that time, which have led to enormously varied interactions with algebra, analysis, and geometry. Workers in many of these areas have often lamented the lack of a single source that surveys surgery theory and its applications. Indeed, no one person could write such a survey.

The sixtieth birthday of C. T. C. Wall, one of the leaders of the founding generation of surgery theory, provided an opportunity to rectify the situation and produce a comprehensive book on the subject. Experts have written state-of-the-art reports that will be of broad interest to all those interested in topology, not only graduate students and mathematicians, but mathematical physicists as well.

Contributors include J. Milnor, S. Novikov, W. Browder, T. Lance, E. Brown, M. Kreck, J. Klein, M. Davis, J. Davis, I. Hambleton, L. Taylor, C. Stark, E. Pedersen, W. Mio, J. Levine, K. Orr, J. Roe, J. Milgram, and C. Thomas.

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Product Details

  • ISBN-13: 9780691049373
  • Publisher: Princeton University Press
  • Publication date: 12/21/1999
  • Series: Annals of Mathematics Studies
  • Pages: 448
  • Product dimensions: 6.36 (w) x 9.52 (h) x 1.32 (d)

Table of Contents

Preface
C.T.C. Wall's contributions to the topology of manifolds 3
C.T.C. Wall's publication list 17
Classification of (n - 1)-connected 2n-dimensional manifolds and the discovery of exotic spheres 25
Surgery in the 1960's 31
Differential topology of higher dimensional manifolds 41
Differentiable structures on manifolds 73
The Kervaire invariant and surgery theory 105
A guide to the classification of manifolds 121
Poincare duality spaces 135
Poincare duality groups 167
Manifold aspects of the Novikov Conjecture 195
A guide to the calculation of the surgery obstruction groups for finite groups 225
Surgery theory and infinite fundamental groups 275
Continuously controlled surgery theory 307
Homology manifolds 323
A survey of applications of surgery to knot and link theory 345
Surgery and C-algebras 365
The classification of Aloff-Wallach manifolds and their generalizations 379
Elliptic cohomology 409
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