Dugger, DanielMay, Clover2018-09-062018-09-062018-09-06https://hdl.handle.net/1794/23748Let 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-USAll Rights Reserved.Electronic Thesis or Dissertation