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

Abstract

We specify exterior generators for ${\pi }_{\ast }THH(MU)={\pi }_{\ast }(MU)\otimes E({\lambda }_n^{\prime }\mid n\ge 1)$ and ${\pi }_{\ast }THH(BP)={\pi }_{\ast }(BP)\otimes E({\lambda }_n\mid n\ge 1)$, and calculate the action of the $\sigma$-operator on these graded rings. In particular, $\sigma ({\lambda }_n^{\prime })=0$ and $\sigma ({\lambda }_n)=0$, while the actions on ${\pi }_{\ast }(MU)$ and ${\pi }_{\ast }(BP)$ are expressed in terms of the right units ${\eta }_R$ in the Hopf algebroids $({\pi }_{\ast }(MU),{\pi }_{\ast }(MU\wedge MU))$ and $({\pi }_{\ast }(BP),{\pi }_{\ast }(BP\wedge BP))$, respectively.

This paper has been accepted for publication by the Journal of Topology

References in corpus (2)

• Topological Hochschild homology and the Hasse-Weil zeta function
• Cubical and cosimplicial descent

Cited by in corpus (2)

• Algebraic K-theory of elliptic cohomology
• Topological Hochschild homology of truncated Brown-Peterson spectra I