The structure of Ω*(Z p), p an odd prime

Abstract

We begin now our study of maps of odd prime period. The primary problem is to compute the structure of the group Ω n (Z p ) of bordism classes [T, M n ] where T is a fixed point free orientation preserving diffeomorphism of period p on the closed oriented manifold M n . The bordism spectral sequence of B(Z p ) is trivial, and this gives the order of the reduced groups \(\tilde \Omega _n \left( {Z_p } \right)\). To obtain the precise structure is harder. It is solved here by geometric methods using certain maps of period p on P p-1 (C) with isolated fixed points. We obtain finally in (36.5) the complete additive structure of Ω*(Z p ). We go on in section 37 to study Ω*(Z pk ).