Surveys on Surgery Theory (AM-145), Volume 1 :Papers Dedicated to C. T. C. Wall. (AM-145) ( Annals of Mathematics Studies )

Publication subTitle :Papers Dedicated to C. T. C. Wall. (AM-145)

Publication series :Annals of Mathematics Studies

Author: Cappell Sylvain;Ranicki Andrew;Rosenberg Jonathan;  

Publisher: Princeton University Press‎

Publication year: 2014

E-ISBN: 9781400865192

P-ISBN(Paperback): 9780691049373

Subject: O189 topology (geometry of situation)

Keyword: 数学

Language: ENG

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Description

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.

Chapter

Differentiable structures on manifolds

The Kervaire invariant and surgery theory

A guide to the classification of manifolds

Poincaré duality spaces

Poincaré duality groups

Manifold aspects of the Novikov Conjecture

A guide to the calculation of the surgery obstruction groups for finite groups

Surgery theory and infinite fundamental groups

Continuously controlled surgery theory

Homology manifolds

A survey of applications of surgery to knot and link theory

Surgery and C* -algebras

The classification of Aloff-Wallach manifolds and their generalizations

Elliptic cohomology

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