The oriented bordism of 𝑍_{2^{𝑘}} actions

Abstract

Let R 2 {R_2} be the subring of the rationals given by R 2 = Z [ 1 / 2 ] {R_2} = Z[1/2] . It is shown that for G = Z 2 k G = {Z_{{2^k}}} the bordism group of orientation preserving G G actions on oriented manifolds tensored with R 2 {R_2} is a free Ω ∗ ⊗ R 2 {\Omega _ \ast } \otimes {R_2} module on even dimensional generators (where Ω ∗ {\Omega _ \ast } is the oriented bordism ring).