Analytic torsion of nilmanifolds with (2,3,5) distributions

TL;DR

This paper demonstrates that for certain 5-dimensional nilmanifolds with rank two distributions, the analytic torsion of the Rumin complex matches the classical Ray-Singer torsion, linking geometric analysis and topological invariants.

Contribution

It establishes the equality of analytic torsion and Ray-Singer torsion for a specific class of nilmanifolds with (2,3,5) distributions, providing new insights into their geometric and topological properties.

Findings

Analytic torsion of Rumin complex equals Ray-Singer torsion

Valid for 5-dimensional nilmanifolds with rank two distributions

Links geometric analysis with topological invariants

Abstract

We consider generic rank two distributions on 5-dimensional nilmanifolds, and show that the analytic torsion of their Rumin complex coincides with the Ray-Singer torsion.