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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Für Beruf und Forschung
Für höhere Schule und Studium
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Höhe: 229 mm
Breite: 152 mm
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ISBN-13
978-0-691-04937-3 (9780691049373)
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Schweitzer Klassifikation
Sylvain Cappell is Professor of Mathematics at New York University and has received Sloan Foundation and Guggenheim awards. Andrew Ranick is Professor of Mathematics at the University of Edinburgh. He is the author of several books, including Exact Sequences in the Algebraic Theory of Surgery (Princeton). Jonathan Rosenberg is Professor of Mathematics at the University of Maryland. He has authored or coauthored several books on K-theory, topology, Lie group representations, and mathematical software.
The Editors Preface vii The Editors C. T. C. Wall's contributions to the topology of manifolds 3 C. T. C. Wall's publication list 17 J. Milnor Classification of (n - l)-connected 2n-dimensional manifolds and the discovery of exotic spheres 25 S. Novikov Surgery in the 1960's 31 W. Browder Differential topology of higher dimensional manifolds 41 T. Lance Differentiable structures on manifolds 73 E. Brown The Kervaire invariant and surgery theory 105 A Kreck A guide to the classification of manifolds 121 J. Klein Poincare duality spaces 135 A Davis Poincare duality groups 167 J. Davis Manifold aspects of the Novikov Conjecture 195 I. Hambleton and L. Taylor A guide to the calculation of the surgery obstruction groups for finite groups 225 C. Stark Surgery theory and infinite fundamental groups 275 E. Pedersen Continuously controlled surgery theory 307 W. Mio Homology manifolds 323 J. Levine and K. Orr A survey of applications of surgery to knot and link theory 345 J. Roe Surgery and C*-algebras 365 R. J. Milgram The classification of Aloff-Wallach manifolds and their generalizations 379 C. Thomas Elliptic cohomology 409
