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Clover May: Decomposing C2-equivariant spectra

Time: Tue 2022-11-29 10.15

Location: Albano, house 1, Cramer room

Participating: Clover May (NTNU)

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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.