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arXiv · 1905.06698

The circle action on topological Hochschild homology of complex cobordism and the Brown-Peterson spectrum

John Rognes
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Abstract

We specify exterior generators for $π_* THH(MU) = π_*(MU) \otimes E(λ'_n \mid n\ge1)$ and $π_* THH(BP) = π_*(BP) \otimes E(λ_n \mid n\ge1)$, and calculate the action of the $σ$-operator on these graded rings. In particular, $σ(λ'_n) = 0$ and $σ(λ_n) = 0$, while the actions on $π_*(MU)$ and $π_*(BP)$ are expressed in terms of the right units $η_R$ in the Hopf algebroids $(π_*(MU), π_*(MU \wedge MU))$ and $(π_*(BP), π_*(BP \wedge BP))$, respectively.

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John Rognes. 2019-12-06. The circle action on topological Hochschild homology of complex cobordism and the Brown-Peterson spectrum. https://doi.org/10.1112/topo.12141

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