Abstract: | The classical surgery theory (see 5] and 23]) computes the structure set Sm (M, rel ?) of manifolds homotopy equivalent to M relative to the boundary. Siebenmann showed that in topological category, the structure set is 4-periodic: Sm(M, rel ?) ? Sm+4(M × D4, rel ?) up to a copy of ?; see 12]. Cappell and Weinberger gave a geometric interpretation of this periodicity in 8]. By using Weinberger's stratified surgery theory (see 24]), we extend this to an equivariant periodicity result for topological manifolds with homotopically stratified actions by compact Lie groups, with D4 replaced by the unit ball of certain group representations. In particular, if G is an odd order group acting on a topological manifold M, then the equivariant stable structure sets satisfy S (M, rel ?) ? S (M × D(?4 ? ?G), rel ?) up to copies of ?. © 1993 John Wiley & Sons, Inc. |