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arXiv · 2410.15903

Global Homotopies for Differential Hochschild Cohomologies

Marvin Dippell·Chiara Esposito·Jonas Schnitzer·Stefan Waldmann
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Abstract

We construct explicit global homotopies for differential Hochschild cochains in differential geometry, thereby upgrading the classical Hochschild-Kostant-Rosenberg map to a deformation retract. Our approach combines two key techniques: a symbol calculus from differential geometry and a coalgebraic version of the van Est theorem. To demonstrate its effectiveness, we develop deformation retracts in several related settings, including principal bundles and invariant contexts. As a byproduct, we recover the classical Hochschild-Kostant-Rosenberg theorem and compute previously inaccessible Hochschild cohomologies.

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Marvin Dippell, Chiara Esposito, Jonas Schnitzer, Stefan Waldmann. 2024-10-21. Global Homotopies for Differential Hochschild Cohomologies. https://arxiv.org/abs/2410.15903

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