- Volume
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v. 1 : cloth ISBN 9780691049373
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.
Table of Contents
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
- Volume
-
v. 1 : pbk ISBN 9780691049380
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.
Table of Contents
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
- Volume
-
v. 2 : cloth ISBN 9780691088143
Description
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. Weinbergen, B. Hughes, S. Stolz, R. Kirby, L. Taylor, and F. Quinn.
Table of Contents
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
- Volume
-
v. 2 : pbk ISBN 9780691088150
Description
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.
Table of Contents
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
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