On the Coefficients of some Nonabelian Equivariant Cohomology Theories

Abstract

In this thesis, we give a complete calculation of the coefficients of ordinary equivariant cohomology with constant coefficients, graded by the real representation ring of a finite group, where the group is the dihedral group of order 2p for an odd prime p, and when the group is the quaternion group. Another independent topic will be equivariant complex cobordism. We calculate the coefficient ring of homotopical equivariant complex cobordism for the symmetric group on three elements. We also study the relation between the coefficient ring of equivariant complex cobordism and the universal Lazard ring of equivariant formal group laws for finite abelian groups, and prove a result generalizing classical Quillen's Theorem.