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2008 Topological Hochschild homology and cohomology of $A_\infty$ ring spectra
Vigleik Angeltveit
Geom. Topol. 12(2): 987-1032 (2008). DOI: 10.2140/gt.2008.12.987

Abstract

Let A be an A ring spectrum. We use the description from our preprint [math.AT/0612165] of the cyclic bar and cobar construction to give a direct definition of topological Hochschild homology and cohomology of A using the Stasheff associahedra and another family of polyhedra called cyclohedra. This construction builds the maps making up the A structure into THH(A), and allows us to study how THH(A) varies over the moduli space of A structures on A.

As an example, we study how topological Hochschild cohomology of Morava K–theory varies over the moduli space of A structures and show that in the generic case, when a certain matrix describing the noncommutativity of the multiplication is invertible, topological Hochschild cohomology of 2–periodic Morava K–theory is the corresponding Morava E–theory. If the A structure is “more commutative”, topological Hochschild cohomology of Morava K–theory is some extension of Morava E–theory.

Citation

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Vigleik Angeltveit. "Topological Hochschild homology and cohomology of $A_\infty$ ring spectra." Geom. Topol. 12 (2) 987 - 1032, 2008. https://doi.org/10.2140/gt.2008.12.987

Information

Received: 5 April 2007; Accepted: 8 February 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1149.55006
MathSciNet: MR2403804
Digital Object Identifier: 10.2140/gt.2008.12.987

Subjects:
Primary: 55P43
Secondary: 18D50, 55S35

Rights: Copyright © 2008 Mathematical Sciences Publishers

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