Global Homotopies for Differential Hochschild Cohomologies
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915968508231680 |
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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 |