A spectrum-level Hodge filtration on topological Hochschild homology

Abstract

We define a functorial spectrum-level filtration on the topological Hochschild homology of any commutative ring spectrum $R$, and more generally the factorization homology $R\otimes X$ for any space $X$, echoing algebraic constructions of Loday and Pirashvili. We investigate the properties of this filtration and show that it breaks THH up into common eigenspectra of the Adams operations.

References in corpus (7)

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• Dualizing cartesian and cocartesian fibrations
• Day convolution for infinity-categories
• Factorization homology of stratified spaces
• Structured singular manifolds and factorization homology
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• A note on commutative algebras and their modules in quasicategories

Cited by in corpus (2)

• Model $\infty$-categories I: some pleasant properties of the $\infty$-category of simplicial spaces
• A note on commutative algebras and their modules in quasicategories