五维一般二阶分布的解析扭转。

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of Geometric Analysis Pub Date : 2022-01-01 Epub Date: 2022-07-26 DOI:10.1007/s12220-022-00987-z

Stefan Haller

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引用次数: 0

摘要

我们提出了闭合5流形上与一般秩2分布相关的Rumin复合体的解析扭转。这种扭转在庞加莱对偶和有限覆盖下的表现与预期一致。我们建立了异常公式，用局部量上的积分来表示对亚黎曼度规和2平面束的依赖。对于某些零流形，我们能够证明这种扭转与Ray-Singer解析扭转一致，直到一个常数。

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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 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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来源期刊

Journal of Geometric Analysis 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

290

审稿时长

3 months

期刊介绍： JGA publishes both research and high-level expository papers in geometric analysis and its applications. There are no restrictions on page length.