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Surgery theory, the basis for the classification theory of manifolds, is now about forty years old. The sixtieth birthday (on December 14, 1996) of C.T.C. Wall, a leading member of the subject's founding generation, led the editors of this volume to reflect on the extraordinary accomplishments of surgery theory as well as its current enormously varied interactions with algebra, analysis, and geometry.
Workers in many of these areas have often lamented the lack of a single source surveying surgery theory and its applications. Because no one person could write such a survey, the editors asked a variety of experts to report on the areas of current interest. This is the second of two volumes resulting from that collective effort. It will be useful to topologists, to other interested researchers, and to advanced students. The topics covered include current applications of surgery, Wall's finiteness obstruction, algebraic surgery, automorphisms and embeddings of manifolds, surgery theoretic methods for the study of group actions and stratified spaces, metrics of positive scalar curvature, and surgery in dimension four.
In addition to the editors, the contributors are S. Ferry, M. Weiss, B. Williams, T. Goodwillie, J. Klein, S. Weinberger, B. Hughes, S. Stolz, R. Kirby, L. Taylor, and F. Quinn.
Sommario
Preface vii
Surgery theory today--what it is and where it's going by J. Rosenberg 3
Reflections on C. T. C. Wall's work on cobordism by J. Rosenberg 49
A survey of Wall's finiteness obstruction by S. Ferry and A. Ranicki 63
An introduction to algebraic surgery by A. Ranicki 81
Automorphiams of manifolds by M. Weiss and B. Williams 165
Spaces smooth embeddings, disjunction and surgery by T. Goodwillie, J. Klein and M. Weiss 221
Surgery and stratified spaces by B. Hughes and S. Weinberger 319
Metrics of positive scalar curvature and connections with surgery by J. Rosenberg and S. Stolz 353
A survey of 4-manifolds through the eyes of surgery by R. Kirby and L. Taylor 387
Problems in 4-dimensional topology by F. Quinn 423
Info autore
Edited by Sylvain Cappell, Andrew Ranicki, & Jonathan Rosenberg
Riassunto
Surgery theory is the basis for the classification theory of manifolds. This title reflects on the accomplishments of surgery theory as well as its varied interactions with algebra, analysis, and geometry. It covers the topics that include applications of surgery, Wall's finiteness obstruction, algebraic surgery, and surgery in dimension four.
