Some notes on analytic torsion of the Rumin complex on contact manifolds

Abstract

We propose a definition for analytic torsion of the Rumin complex on contact manifolds. This is given by the derivative at zero of a well-chosen combination of zeta functions of a fourth-order modified Rumin Laplacian. The regular value at zero (before differentiation) of this well-chosen combination of zeta functions is shown to be a contact invariant. The variation of our analytic torsion is given as the integral of local terms, together with a global term coming from the null-space of the Laplacian.

This paper has been withdrawn by the author, due a crucial error on page 8. A corrected and extended version of this paper appears at arXiv:0802.0123

References in corpus (2)

• Noncommutative residue for Heisenberg manifolds. Applications in CR and contact geometry
• Diabatic Limit, Eta Invariants and Cauchy-Riemann Manifolds of Dimension 3

Cited by in corpus (2)

• Future Directions of Research in Geometry: A Summary of the Panel Discussion at the 2007 Midwest Geometry Conference
• Approximately Einstein ACH metrics, volume renormalization, and an invariant for contact manifolds