# A generalization of analytic torsion via differential forms on spaces of metrics

## TL;DR

This paper introduces multi-torsion, a new spectral invariant that generalizes analytic torsion by utilizing differential forms on spaces of metrics, and proves its metric-independence under certain conditions.

## Contribution

The paper defines multi-torsion for manifolds with a local geometric product structure and establishes its metric-independence, extending the concept of analytic torsion.

## Key findings

- Multi-torsion generalizes Ray-Singer analytic torsion.
- Multi-torsion is shown to be metric-independent.
- The approach uses a generalized Stokes' theorem argument.

## Abstract

We introduce multi-torsion, a spectral invariant generalizing Ray-Singer analytic torsion. We define multi-torsion for compact manifolds with a certain local geometric product structure that gives a bigrading on differential forms. We prove that multi-torsion is metric-independent in a suitable sense. Our definition of multi-torsion is inspired by an interpretation of each of analytic torsion and the eta invariant as a regularized integral of a closed differential form on a space of metrics on a vector bundle or on a space of elliptic operators. We generalize the Stokes' theorem argument explaining the dependence of torsion and eta on the geometric data used to define them to the local product setting to prove our metric-independence theorem for multi-torsion.