Equivariant Complex Cobordism.

Abstract

We begin with a development of equivariant stable homotopy theory relevant to our work, including a new result on shift desuspension of suspension spectra. We then build on existing techniques of Kriz to compute the equivariant complex cobordism ring of a finite abelian group. Methods of isotropy separation via Tate diagrams are heavily employed, and the key computational tool is the Isotropy Separation Spectral Sequence that is here introduced. We also consider equivariant formal group laws. There is a G-equivariant formal group law corresponding to any complex oriented G-equivariant spectrum E. Since the equivariant complex cobordism spectrum has a canonical complex orientation, there is a corresponding equivariant formal group law. We compute the G-equivariant formal group law corresponding to this spectrum for G finite abelian. This computation is a step in the direction of Greenlees' Conjecture that this equivariant formal group law is algebraically universal.