# Clover May: Decomposing C2-equivariant spectra

**Time: **
Tue 2022-11-29 10.15

**Location: **
Albano, house 1, Cramer room

**Participating: **
Clover May (NTNU)

**Abstract:**

Computations in RO(G)-graded Bredon cohomology can be challenging and are not well understood, even for G=C_2, the cyclic group of order two. A recent structure theorem for RO(C_2)-graded cohomology with Z/2 coefficients substantially simplifies computations. The structure theorem says the cohomology of any finite C2-CW complex decomposes as a direct sum of two basic pieces: cohomologies of representation spheres and cohomologies of spheres with the antipodal action. This decomposition lifts to a splitting at the spectrum level. In joint work with Dan Dugger and Christy Hazel we extend this result to a classification of compact modules over the genuine equivariant Eilenberg-MacLane spectrum HZ/2.