A spectrum-level Hodge filtration on topological Hochschild homology
Saul Glasman
TL;DR
This paper introduces a new spectrum-level filtration on topological Hochschild homology (THH) for commutative ring spectra, revealing its structure through eigenspectra of Adams operations and generalizing algebraic filtrations.
Contribution
It defines a functorial spectrum-level filtration on THH and factorization homology, connecting algebraic constructions with topological and spectral properties.
Findings
Filtration decomposes THH into eigenspectra of Adams operations
Generalizes algebraic Loday and Pirashvili filtrations to spectra
Provides new insights into the structure of topological Hochschild homology
Abstract
We define a functorial spectrum-level filtration on the topological Hochschild homology of any commutative ring spectrum , and more generally the factorization homology for any space , 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra