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Main Authors: Dippell, Marvin, Esposito, Chiara, Schnitzer, Jonas, Waldmann, Stefan
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2410.15903
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author Dippell, Marvin
Esposito, Chiara
Schnitzer, Jonas
Waldmann, Stefan
author_facet Dippell, Marvin
Esposito, Chiara
Schnitzer, Jonas
Waldmann, Stefan
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2410_15903
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Global Homotopies for Differential Hochschild Cohomologies
Dippell, Marvin
Esposito, Chiara
Schnitzer, Jonas
Waldmann, Stefan
Differential Geometry
Quantum Algebra
53C05, 53D55, 13D03
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.
title Global Homotopies for Differential Hochschild Cohomologies
topic Differential Geometry
Quantum Algebra
53C05, 53D55, 13D03
url https://arxiv.org/abs/2410.15903