Analytic Torsion of Generic Rank Two Distributions in Dimension Five

Stefan Haller

doi:10.1007/s12220-022-00987-z

Analytic Torsion of Generic Rank Two Distributions in Dimension Five

Stefan Haller

Department of Mathematics

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

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.

Original language	English
Article number	248
Number of pages	66
Journal	The Journal of Geometric Analysis
Volume	32
DOIs	https://doi.org/10.1007/s12220-022-00987-z
Publication status	Published - 26 Jul 2022

Austrian Fields of Science 2012

101002 Analysis
101006 Differential geometry

Keywords

Analytic torsion
Rumin compelx
Rockland complex
Generic rank two distribution
(2,3,5) distribution
Sub-Riemannian geometry
Rumin complex
EXISTENCE
COMPLEX
OVERTWISTED CONTACT STRUCTURES
CHEEGER
THEOREM
REPRESENTATION
CLASSIFICATION
(2
5) distribution
3
DIFFERENTIAL FORMS
R-TORSION
GEOMETRY

Access to Document

10.1007/s12220-022-00987-zLicence: CC BY 4.0

https://phaidra.univie.ac.at/o:1646054Licence: CC BY 4.0

Cite this

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title = "Analytic Torsion of Generic Rank Two Distributions in Dimension Five",

abstract = "We propose an analytic torsion for the Rumin complex associated with generic ranktwo distributions on closed 5-manifolds. This torsion behaves as expected with respectto Poincar{\'e} duality and finite coverings. We establish anomaly formulas, expressingthe dependence on the sub-Riemannian metric and the 2-plane bundle in terms ofintegrals over local quantities. For certain nilmanifolds, we are able to show that thistorsion coincides with the Ray–Singer analytic torsion, up to a constant.",

keywords = "Analytic torsion, Rumin compelx, Rockland complex, Generic rank two distribution, (2,3,5) distribution, Sub-Riemannian geometry, Rumin complex, EXISTENCE, COMPLEX, OVERTWISTED CONTACT STRUCTURES, CHEEGER, THEOREM, REPRESENTATION, CLASSIFICATION, (2, 5) distribution, 3, DIFFERENTIAL FORMS, R-TORSION, GEOMETRY",

author = "Stefan Haller",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s).",

year = "2022",

month = jul,

day = "26",

doi = "10.1007/s12220-022-00987-z",

language = "English",

volume = "32",

journal = "Journal of Geometric Analysis",

issn = "1050-6926",

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TY - JOUR

T1 - Analytic Torsion of Generic Rank Two Distributions in Dimension Five

AU - Haller, Stefan

PY - 2022/7/26

Y1 - 2022/7/26

N2 - We propose an analytic torsion for the Rumin complex associated with generic ranktwo distributions on closed 5-manifolds. This torsion behaves as expected with respectto Poincaré duality and finite coverings. We establish anomaly formulas, expressingthe dependence on the sub-Riemannian metric and the 2-plane bundle in terms ofintegrals over local quantities. For certain nilmanifolds, we are able to show that thistorsion coincides with the Ray–Singer analytic torsion, up to a constant.

AB - We propose an analytic torsion for the Rumin complex associated with generic ranktwo distributions on closed 5-manifolds. This torsion behaves as expected with respectto Poincaré duality and finite coverings. We establish anomaly formulas, expressingthe dependence on the sub-Riemannian metric and the 2-plane bundle in terms ofintegrals over local quantities. For certain nilmanifolds, we are able to show that thistorsion coincides with the Ray–Singer analytic torsion, up to a constant.

KW - Analytic torsion

KW - Rumin compelx

KW - Rockland complex

KW - Generic rank two distribution

KW - (2,3,5) distribution

KW - Sub-Riemannian geometry

KW - Rumin complex

KW - EXISTENCE

KW - COMPLEX

KW - OVERTWISTED CONTACT STRUCTURES

KW - CHEEGER

KW - THEOREM

KW - REPRESENTATION

KW - CLASSIFICATION

KW - (2

KW - 5) distribution

KW - 3

KW - DIFFERENTIAL FORMS

KW - R-TORSION

KW - GEOMETRY

UR - http://www.scopus.com/inward/record.url?scp=85134835736&partnerID=8YFLogxK

U2 - 10.1007/s12220-022-00987-z

DO - 10.1007/s12220-022-00987-z

M3 - Article

VL - 32

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

SN - 1050-6926

M1 - 248

ER -

Analytic Torsion of Generic Rank Two Distributions in Dimension Five

Abstract

Austrian Fields of Science 2012

Keywords

Access to Document

Other files and links

Fingerprint

Isoperimetr. Struktur v Anfangs

Analytic torsion of filtered manifolds

Regularized determinants of the Rumin complex on nilmanifolds with (2,3,5) geometry

Analytic torsion of the Rumin complex on filtered 5-manifolds with growth vector (2,3,5)

Analytic torsion of (2,3,5) geometries

Cite this

Analytic Torsion of Generic Rank Two Distributions in Dimension Five

Abstract

Austrian Fields of Science 2012

Keywords

Access to Document

Other files and links

Fingerprint

Projects

Isoperimetr. Struktur v Anfangs

Analytic torsion of filtered manifolds

Activities

Regularized determinants of the Rumin complex on nilmanifolds with (2,3,5) geometry

Analytic torsion of the Rumin complex on filtered 5-manifolds with growth vector (2,3,5)

Analytic torsion of (2,3,5) geometries

Cite this