An equivariant Quillen theorem

Abstract

A classical theorem due to Quillen (1969) identifies the unitary bordism ring with the Lazard ring, which represents the universal one-dimensional commutative formal group law. We prove an equivariant generalization of this result by identifying the homotopy theoretic Z/2-equivariant unitary bordism ring, introduced by tom Dieck (1970), with the Z/2-equivariant Lazard ring, introduced by Cole–Greenlees–Kriz (2000). Our proof combines a computation of the homotopy theoretic Z/2-equivariant unitary bordism ring due to Strickland (2001) with a detailed investigation of the Z/2-equivariant Lazard ring.