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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Basu, S., Ghosh, S. Computations in \(C_{pq}\)-Bredon cohomology. Math. Z. 293, 1443–1487 (2019). https://doi.org/10.1007/s00209-019-02248-2
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DOI: https://doi.org/10.1007/s00209-019-02248-2