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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.

Sub-Riemannian Limit of the Differential Form Heat Kernels of Contact Manifolds