The $RO(\mathcal{K})$-graded Coefficients of $H\underline{A}$

Fuente: arXiv
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Main Author: Keyes, Jesse
Format: Preprint
Published: 2025
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author Keyes, Jesse
author_facet Keyes, Jesse
contents In $G$-equivariant stable homotopy theory, it is known that the equivariant Eilenberg-Mac Lane spectra representing ordinary equivariant cohomology have nontrivial $RO(G)$-graded homotopy corresponding to the equivariant (co)homology of representation spheres. We will compute the universal case of this ordinary $RO(G)$-graded homotopy in the case of $G=\mathcal{K}$, where $\mathcal{K}$ is the Klein-four group. In particular, we will compute a subring of the $RO(\mathcal{K})$-graded homotopy of $H\underline{A}$ for $\underline{A}$ the Burnside Mackey functor.
format Preprint
id arxiv_https___arxiv_org_abs_2503_03173
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The $RO(\mathcal{K})$-graded Coefficients of $H\underline{A}$
Keyes, Jesse
Algebraic Topology
In $G$-equivariant stable homotopy theory, it is known that the equivariant Eilenberg-Mac Lane spectra representing ordinary equivariant cohomology have nontrivial $RO(G)$-graded homotopy corresponding to the equivariant (co)homology of representation spheres. We will compute the universal case of this ordinary $RO(G)$-graded homotopy in the case of $G=\mathcal{K}$, where $\mathcal{K}$ is the Klein-four group. In particular, we will compute a subring of the $RO(\mathcal{K})$-graded homotopy of $H\underline{A}$ for $\underline{A}$ the Burnside Mackey functor.
title The $RO(\mathcal{K})$-graded Coefficients of $H\underline{A}$
topic Algebraic Topology
url https://arxiv.org/abs/2503.03173