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

Eric Hogle; Clover May

doi:10.1016/j.topol.2020.107413

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arXiv · 2005.07300

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

Eric Hogle·Clover May

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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 fixed-set dimension. We give a counterexample showing the theorem does not hold for locally finite complexes.

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BibTeX RIS

Eric Hogle, Clover May. 2020-05-14. The freeness theorem for equivariant cohomology of Rep($C_2$)-complexes. https://doi.org/10.1016/j.topol.2020.107413

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