Surveys on Surgery Theory

by Wall, C. T. C.; Ranicki, Andrew; Rosenberg, Jonathan; Cappell, Sylvain

• ISBN13: 9780691049380
• ISBN10: 0691049386
• Format: Paperback
• Copyright: 1999-12-21
• Publisher: Princeton Univ Pr

Summary

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
C. T. C. Wall's contributions to the topology of manifolds	3	(14)
C. T. C. Wall's publication list	17	(8)
Classification of (n -- 1)-connected 2n-dimensional manifolds and the discovery of exotic spheres	25	(6)
J. Milnor
Surgery in the 1960's	31	(10)
S. Novikov
Differential topology of higher dimensional manifolds	41	(32)
W. Browder
Differentiable structures on manifolds	73	(32)
T. Lance
The Kervaire invariant and surgery theory	105	(16)
E. Brown
A guide to the classification of manifolds	121	(14)
M. Kreck
Poincare duality spaces	135	(32)
J. Klein
Poincare duality groups	167	(28)
M. Davis
Manifold aspects of the Novikov Conjecture	195	(30)
J. Davis
A guide to the calculation of the surgery obstruction groups for finite groups	225	(50)
I. Hambleton
L. Taylor
Surgery theory and infinite fundamental groups	275	(32)
C. Stark
Continuously controlled surgery theory	307	(16)
E. Pedersen
Homology manifolds	323	(22)
W. Mio
A survey of applications of surgery to knot and link theory	345	(20)
J. Levine
K. Orr
Surgery and C*-algebras	365	(14)
J. Roe
The classification of Aloff-Wallach manifolds and their generalizations	379	(30)
R. J. Milgram
Elliptic cohomology	409
C. Thomas