Transversality Obstructions and Equivariant Bordism for G=Z/2

Abstract

In this paper we compute homotopical equivariant bordism for the group ${\bf Z/2}$, namely $MO^{\bf Z/2}$, geometric equivariant bordism $Ω^{\bf Z/2}_*$, and their quotient as modules over geometric bordism. This quotient is a module of stable transversality obstructions. In doing these computations, we use the techniques the author developed in the complex setting. Because we are working in the real setting only with Z/2, these techniques simplify greatly.