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Hopf algebra structure on topological Hochschild homology

Vigleik Angeltveit·John Rognes
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Abstract

The topological Hochschild homology THH(R) of a commutative S-algebra (E_infty ring spectrum) R naturally has the structure of a commutative R-algebra in the strict sense, and of a Hopf algebra over R in the homotopy category. We show, under a flatness assumption, that this makes the Boekstedt spectral sequence converging to the mod p homology of THH(R) into a Hopf algebra spectral sequence. We then apply this additional structure to the study of 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, by means of the cyclotomic trace map to topological cyclic homology.

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BibTeXRIS

Vigleik Angeltveit, John Rognes. 2005-10-17. Hopf algebra structure on topological Hochschild homology. https://doi.org/10.2140/agt.2005.5.1223

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