Ray-Singer Torsion and the Rumin Laplacian on Lens Spaces

TL;DR

This paper explicitly computes the analytic torsion functions for the Rumin complex on lens spaces using Hurwitz zeta functions, revealing their vanishing at zero and establishing a relation with Ray-Singer torsion.

Contribution

It provides explicit formulas for the analytic torsion functions on lens spaces and links them to Ray-Singer torsion, advancing understanding of torsion invariants.

Findings

Analytic torsion functions vanish at the origin.

Explicit formulas relate Rumin and Ray-Singer torsions.

Established connections between different torsion invariants.

Abstract

We express explicitly the analytic torsion functions associated with the Rumin complex on lens spaces in terms of the Hurwitz zeta function. In particular, we find that the functions vanish at the origin and determine the analytic torsions. Moreover, we have a formula between this torsion and the Ray-Singer torsion.