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 ).