Sarah Petersen

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math.AT2026

The real Brown-Peterson homology of $Ω^{ρ} S^{ρ + 1}$

Christian Carrick, Bertrand Guillou, Sarah Petersen

We compute the $R O (C_{2})$ -graded real Brown--Peterson homology of the representation-loop space $Ω^{ρ} S^{ρ + 1}$ , where $ρ$ is the regular representation of the cyclic group of order t…

math.AT2025

Splittings of truncated motivic Brown--Peterson cooperations algebras

Jackson Morris, Sarah Petersen, Elizabeth Tatum

We construct spectrum-level splittings of $B P G L ⟨ 1 ⟩ \land B P G L ⟨ 1 ⟩$ at all primes $p$ , where $B P G L ⟨ 1 ⟩$ is the first truncated motivic Br…

math.AT2025

Graphs arising from the dual Steenrod algebra

Connor Elliott, Courtney Hauf, Kai Morton +2

We extend Wood's graph theoretic interpretation of certain quotients of the mod $2$ dual Steenrod algebra to quotients of the mod $p$ dual Steenrod algebra where $p$ is an odd prim…

math.AT2025

A spectrum-level splitting of the $k u_{R}$ -cooperations algebra

Guchuan Li, Sarah Petersen, Elizabeth Tatum

In the 1980's, Mahowald and Kane used integral Brown--Gitler spectra to decompose $k u \land k u$ as a sum of finitely generated $k u$ -module spectra. This splitting, along with an a…

math.AT2024

Equivariant Witt Complexes and Twisted Topological Hochschild Homology

Anna Marie Bohmann, Teena Gerhardt, Cameron Krulewski +2

The topological Hochschild homology of a ring (or ring spectrum) $R$ is an $S^{1}$ -spectrum, and the fixed points of THH( $R$ ) for subgroups $C_{n} \subset S^{1}$ have been widely studied…

The real Brown-Peterson homology of ΩρSρ+1

Splittings of truncated motivic Brown--Peterson cooperations algebras

Graphs arising from the dual Steenrod algebra

A spectrum-level splitting of the kuR​-cooperations algebra

Equivariant Witt Complexes and Twisted Topological Hochschild Homology

The real Brown-Peterson homology of $Ω^{ρ} S^{ρ + 1}$

A spectrum-level splitting of the $k u_{R}$ -cooperations algebra