Sub-Riemannian Limit of the Differential Form Heat Kernels of Contact Manifolds
Sub-Riemannian Limit of the Differential Form Heat Kernels of Contact Manifolds
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DOI：
10.1093/imrn/rnaa270
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发表时间：
2022-04-09
影响因子：
1
通讯作者：
Quan, Hadrian
中科院分区：
文献类型：
--
作者：
Albin, Pierre;Quan, Hadrian
我们研究了具有黎曼度量族的接触流形上的霍奇拉普拉斯算子的热核的行为，黎曼度量族在接触分布的横向方向上爆破。我们应用这一点来分析全局谱不变量的行为，如eta不变和拉普拉斯行列式。特别是，我们证明了接触版本的相对η-不变量和相对解析挠率等于他们的黎曼类似物，因此拓扑。
We study the behavior of the heat kernel of the Hodge Laplacian on a contact manifold endowed with a family of Riemannian metrics that blow-up the directions transverse to the contact distribution. We apply this to analyze the behavior of global spectral invariants such as the eta-invariant and the determinant of the Laplacian. In particular, we prove that contact versions of the relative eta-invariant and the relative analytic torsion are equal to their Riemannian analogues and hence topological.