An HKR theorem for factorization homology

2023/05/01 by Rau-Murthy, Hari
#Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2305.00658

Abstract

We prove a Hochschild-Kostant-Rosenberg theorem ("the HKR theorem") which computes the factorization homology of certain smooth commutative ring spectra. In doing so we fix and generalize a THH computation which was first conceived as the brainchild of McCarthy-Minasian. A direct application of our revised HKR theorem is the higher THH of rational KU.

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• Factorization homology and calculus à la Kontsevich Soibelman
• A factorization homology primer
• A spectrum-level Hodge filtration on topological Hochschild homology
• HKR Theorem for Smooth S-algebras
• The Hopf Rings for KO and KU