A Structure Theorem for RO(C2)-graded Cohomology
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Date
2018-09-06
Authors
May, Clover
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Publisher
University of Oregon
Abstract
Let C2 be the cyclic group of order two. We present a structure theorem for the RO(C2)-graded Bredon cohomology of C2-spaces using coefficients in the constant Mackey functor F2. We show that, as a module over the cohomology of the point, the RO(C2)-graded cohomology of a finite C2-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. The shifts are by elements of RO(C2) corresponding to actual (i.e. non-virtual) C2-representations.