Computations in $C_{pq}$-Bredon cohomology

Samik Basu; Surojit Ghosh

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arXiv · 1612.02159

Computations in $C_{pq}$-Bredon cohomology

Samik Basu·Surojit Ghosh

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Abstract

In this paper, we compute the $RO(C_{pq})$-graded cohomology of $C_{pq}$-orbits. We deduce that in all the cases the Bredon cohomology groups are a function of the fixed point dimensions of the underlying virtual representations. Further, when thought of as a Mackey functor, the same independence result holds in almost all cases. This generalizes earlier computations of Stong and Lewis for the group $C_p$. The computations of cohomology of orbits are used to prove a freeness theorem. The analogous result for the group $C_p$ was proved by Lewis. We demonstrate that certain complex projective spaces and complex Grassmannians satisfy the freeness theorem.

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BibTeX RIS

Samik Basu, Surojit Ghosh. 2016-12-07. Computations in $C_{pq}$-Bredon cohomology. https://arxiv.org/abs/1612.02159

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