TY - JOUR
AU - Davis, James F.
AB - JAMES F. DAVIS [Received 6 September 1982] 1. Introduction Given a degree-one normal map (/,/) : (M",v ) -> (X, £), C. T. C. Wall defined the associated surgery obstruction a(f, f) e L^JLn^X). This obstruction vanishes if and only if (/ , / ) is normally bordant to a simple homotopy equivalence. Using Wall's approach, one must perform preliminary surgery to make / highly connected before the obstruction can be calculated. It is natural to ask for invariants which can be calculated without preliminary surgery. In the even-dimensional case the multisig- nature gives such an invariant. The purpose of this paper is to present an odd-dimensional normal bordism invariant defined without preliminary surgery. This invariant is analogous to the semicharacteristic bordism invariant introduced by Lee [13]. A justification for the normal bordism invariant is that it gives strong restrictions on the homology of a manifold with a free action of a finite group. In particular, it gives a good explanation of Lee's results on free actions of finite groups on spheres. Let I be a (2n + l)-dimensional Poincare complex with fundamental group n. Suppose A is a semisimple ring with involution a \-> a, for a e 
TI - The Surgery Semicharacteristic
JF - Proceedings of the London Mathematical Society
DO - 10.1112/plms/s3-47.3.411
DA - 1983-11-01
UR - https://www.deepdyve.com/lp/wiley/the-surgery-semicharacteristic-2sEJjGV120
SP - 411
EP - 428
VL - s3-47
IS - 3
DP - DeepDyve
ER -