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Dugger, Daniel May, Clover 2018-09-06T21:56:46Z 2018-09-06T21:56:46Z 2018-09-06 https://hdl.handle.net/1794/23748 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. en_US University of Oregon All Rights Reserved. A Structure Theorem for RO(C2)-graded Cohomology Electronic Thesis or Dissertation Ph.D. doctoral Department of Mathematics University of Oregonopen.access