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

2007/04/16 by Neil Seshadri, Seshadri, Neil
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.0704.1982

This paper has been withdrawn by the author, due a crucial error on page 8.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

arxiv created 2008/02/04 · arxiv updated 2009/12/01

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.

Related

• Sobolev mappings and the Rumin complex
• Complex valued analytic torsion and dynamical zeta function on locally symmetric spaces
• A simple construction of the Rumin algebra
• Residue-Torsion and the Laplacian on Riemannian Manifolds
• Harmonic forms and the Rumin complex on Sasakian manifolds