Global Homotopies for Differential Hochschild Cohomologies

2024/10/21 by Dippell, Marvin, Esposito, Chiara, Schnitzer, Jonas +1 · 1 citation
#13D03 #53C05 #53D55 #Differential Geometry (math.DG) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2410.15903

Abstract

We construct global homotopies to compute differential Hochschild cohomologies in differential geometry. This relies on two different techniques: a symbol calculus from differential geometry and a coalgebraic version of the van Est theorem. Not only do we obtain an improved version of the Hochschild-Kostant-Rosenberg theorem but we also compute Hochschild cohomologies for related scenarios, e.g. for principal bundles, and invariant versions.

Cited by

• Classification and Reduction of Homogeneous Star Products

Related

• On the differentials of the Hochschild-Kostant-Rosenberg spectral sequence
• Differential cohomology
• Global Hochschild (co-)homology of singular spaces
• Differential Cohomology: Categories, Characteristic Classes, and Connections
• A Geometric Approach to Hochschild Cohomology of the Exterior Algebra