The freeness theorem for equivariant cohomology of Rep($C_2$)complexes
Abstract
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 $\underline{\mathbb{F}_2}$. 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 fixedset dimension. We give a counterexample showing the theorem does not hold for locally finite complexes.
 Publication:

arXiv eprints
 Pub Date:
 May 2020
 DOI:
 10.48550/arXiv.2005.07300
 arXiv:
 arXiv:2005.07300
 Bibcode:
 2020arXiv200507300H
 Keywords:

 Mathematics  Algebraic Topology
 EPrint:
 32 pages, 21 figures, v2 corrections to the proof of finite type theorem (6.3), v3 accepted version to appear in Topology and its Applications