2021/03/07 by Ishan Levy, Levy, Ishan · 1 citation
Mathematics · #Advanced Topics in Algebra #Advanced Operator Algebra Research #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2103.04457
Hopkins and Mahowald gave a simple description of the mod p Eilenberg Mac Lane spectrum \mathbbFp as the free 𝔼2-algebra with an equivalence of p and 0. We show for each faithful 2-dimensional representation λ of a p-group G that the G-equivariant Eilenberg Mac Lane spectrum \underline\mathbbFp is the free 𝔼λ-algebra with an equivalence of p and 0. This unifies and simplifies recent work of Behrens, Hahn, and Wilson, and extends it to include the dihedral 2-subgroups of O(2). The main new idea is that \underline\mathbbFp has a simple description as a p-cyclonic module over \rmTHH(\mathbbFp). We show our result is the best possible one in that it gives all groups G and representations V such that \underline\mathbbFp is the free 𝔼V-algebra with an equivalence of p and 0.