Computations in Cpq -Bredon cohomology

Article Type

Research Article

Publication Title

Mathematische Zeitschrift

Abstract

In this paper, we compute the RO(Cpq) -graded cohomology of Cpq-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 Cp. The computations of cohomology of orbits are used to prove a freeness theorem. The analogous result for the group Cp was proved by Lewis. We demonstrate that certain complex projective spaces and complex Grassmannians satisfy the freeness theorem.

First Page

1443

Last Page

1487

DOI

10.1007/s00209-019-02248-2

Publication Date

12-1-2019

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