Title:
Hopf algebra structure on topological Hochschild homology
Author(s):
Vigleik Angeltveit and John Rognes
Author's e-mail address:
vigleik@math.mit.edu and rognes@math.uio.no
Abstract:
The topological Hochschild homology THH(R) of a commutative S-algebra
(E-infinity ring spectrum) R naturally has the structure of a Hopf
algebra over R, in the homotopy category. We show that under a flatness
assumption this makes the Bokstedt spectral sequence converging to
the mod p homology of THH(R) into a Hopf algebra spectral sequence.
We then apply this additional structure to study some interesting
examples, including the commutative S-algebras ku, ko, tmf, ju and
j, and to calculate the homotopy groups of THH(ku) and THH(ko) after
smashing with suitable finite complexes. This is part of a program to
make systematic computations of the algebraic K-theory of S-algebras,
using topological cyclic homology.