EVENT DETAILS AND ABSTRACT

Title: A structure theorem for RO(G)-graded cohomology
Speaker: Clover May
Speaker Info: University of Oregon
Brief Description:
Special Note:
Abstract:

Computations of singular cohomology groups are very familiar. An equivariant analogue is RO(G)-graded Bredon cohomology with coefficients in a constant Mackey functor. Computations in this setting are often more challenging and are not well understood. In this talk I will present a structure theorem for RO(C_2)-graded cohomology with \underline{Z/2} coefficients that substantially simplifies computations. The structure theorem says the cohomology of any finite C_2-CW complex decomposes as a direct sum of two basic pieces: shifted copies of the cohomology of a point and shifted copies of the cohomologies of spheres with the antipodal action. I will sketch the proof, which depends on a Toda bracket calculation, and give some examples.