Analytic Torsion of Generic Rank Two Distributions in Dimension Five

We propose an analytic torsion for the Rumin complex associated with generic rank two distributions on closed 5-manifolds. This torsion behaves as expected with respect to Poincaré duality and finite coverings. We establish anomaly formulas, expressing the dependence on the sub-Riemannian metric and...

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Autor principal: Haller, Stefan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9325871/
https://www.ncbi.nlm.nih.gov/pubmed/35912068
http://dx.doi.org/10.1007/s12220-022-00987-z
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author Haller, Stefan
author_facet Haller, Stefan
author_sort Haller, Stefan
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description We propose an analytic torsion for the Rumin complex associated with generic rank two distributions on closed 5-manifolds. This torsion behaves as expected with respect to Poincaré duality and finite coverings. We establish anomaly formulas, expressing the dependence on the sub-Riemannian metric and the 2-plane bundle in terms of integrals over local quantities. For certain nilmanifolds, we are able to show that this torsion coincides with the Ray–Singer analytic torsion, up to a constant.
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spelling pubmed-93258712022-07-28 Analytic Torsion of Generic Rank Two Distributions in Dimension Five Haller, Stefan J Geom Anal Article We propose an analytic torsion for the Rumin complex associated with generic rank two distributions on closed 5-manifolds. This torsion behaves as expected with respect to Poincaré duality and finite coverings. We establish anomaly formulas, expressing the dependence on the sub-Riemannian metric and the 2-plane bundle in terms of integrals over local quantities. For certain nilmanifolds, we are able to show that this torsion coincides with the Ray–Singer analytic torsion, up to a constant. Springer US 2022-07-26 2022 /pmc/articles/PMC9325871/ /pubmed/35912068 http://dx.doi.org/10.1007/s12220-022-00987-z Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Haller, Stefan
Analytic Torsion of Generic Rank Two Distributions in Dimension Five
title Analytic Torsion of Generic Rank Two Distributions in Dimension Five
title_full Analytic Torsion of Generic Rank Two Distributions in Dimension Five
title_fullStr Analytic Torsion of Generic Rank Two Distributions in Dimension Five
title_full_unstemmed Analytic Torsion of Generic Rank Two Distributions in Dimension Five
title_short Analytic Torsion of Generic Rank Two Distributions in Dimension Five
title_sort analytic torsion of generic rank two distributions in dimension five
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9325871/
https://www.ncbi.nlm.nih.gov/pubmed/35912068
http://dx.doi.org/10.1007/s12220-022-00987-z
work_keys_str_mv AT hallerstefan analytictorsionofgenericranktwodistributionsindimensionfive

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