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

摘要

We specify exterior generators in pi*THH(MU)=pi*(MU)circle times E(lambda n ' divide n > 1)and pi*THH(BP)=pi*(BP)circle times E(lambda n divide n > 1), and calculate the action of the sigma-operator on these graded rings. In particular,sigma(lambda n ')=0and sigma(lambda n)=0, while the actions on pi*(MU)and pi*(BP)are expressed in terms of the right units eta Rin the Hopf algebroids(pi*(MU),pi*(MU perpendicular to MU))and(pi*(BP),pi*(BP perpendicular to BP)), respectively.