Sub-Riemannian limit of the differential form heat kernels of contact manifolds

Pierre Albin; Hadrian Quan

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arXiv · 1912.02326

Sub-Riemannian limit of the differential form heat kernels of contact manifolds

Pierre Albin·Hadrian Quan

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Abstract

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.

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Pierre Albin, Hadrian Quan. 2019-12-05. Sub-Riemannian limit of the differential form heat kernels of contact manifolds. https://arxiv.org/abs/1912.02326

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