The RO(K)-graded Coefficients of H\underlineA

2025/03/05 by Jesse Keyes, Keyes, Jesse
Mathematics · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2503.03173

openalex publication_date 2025/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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=K, where K is the Klein-four group. In particular, we will compute a subring of the RO(K)-graded homotopy of H\underlineA for \underlineA the Burnside Mackey functor.

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