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2005 Hopf algebra structure on topological Hochschild homology
Vigleik Angeltveit, John Rognes
Algebr. Geom. Topol. 5(3): 1223-1290 (2005). DOI: 10.2140/agt.2005.5.1223

Abstract

The topological Hochschild homology THH(R) of a commutative S–algebra (E 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 Bökstedt 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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Vigleik Angeltveit. John Rognes. "Hopf algebra structure on topological Hochschild homology." Algebr. Geom. Topol. 5 (3) 1223 - 1290, 2005. https://doi.org/10.2140/agt.2005.5.1223

Information

Received: 16 July 2004; Revised: 21 September 2005; Accepted: 29 September 2005; Published: 2005
First available in Project Euclid: 20 December 2017

zbMATH: 1087.55009
MathSciNet: MR2171809
Digital Object Identifier: 10.2140/agt.2005.5.1223

Subjects:
Primary: 55P43, 55S10, 55S12, 57T05
Secondary: 13D03, 55T15

Rights: Copyright © 2005 Mathematical Sciences Publishers

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