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arXiv · 2104.11407

The $RO(C_4)$ cohomology of the infinite real projective space

Nick Georgakopoulos
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Abstract

Following the Hu-Kriz method of computing the $C_2$ genuine dual Steenrod algebra $(H\mathbf F_2)_{\bigstar}(H\mathbf F_2)$, we calculate the $C_4$ equivariant Bredon cohomology of the classifying space $\mathbf R P^{\infty \rho}=B_{C_4}\Sigma_{2}$ as an $RO(C_4)$ graded Green-functor. We prove that as a module over the homology of a point (which we also compute), this cohomology is not flat. As a result, it can't be used as a test module for obtaining generators in $(H\mathbf F_2)_{\bigstar}(H\mathbf F_2)$ as Hu-Kriz do in the $C_2$ case.

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Nick Georgakopoulos. 2021-04-23. The $RO(C_4)$ cohomology of the infinite real projective space. https://doi.org/10.2140/agt.2024.24.277

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