The freeness theorem for equivariant cohomology of Rep(C_2)-complexes

摘要

Let C-2 be the cyclic group of order two. We show that the RO(C-2)-graded Bredon cohomology of a finite Rep(C-2)-complex is free as a module over the cohomology of a point when using coefficients in the constant Mackey functor F2. This paper corrects some errors in Kronholm's proof of this freeness theorem. It also extends the freeness result to finite type complexes, those with finitely many cells of each fixed-set dimension. We give a counterexample showing the theorem does not hold for locally finite complexes. (c) 2020 Elsevier B.V. All rights reserved.