Computations in C_pq-Bredon cohomology

2016/12/07 by Basu, Samik, Ghosh, Surojit
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1612.02159

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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