Cappell-Miller analytic torsion for manifolds with boundary

TL;DR

This paper extends the Cappell-Miller analytic torsion to manifolds with boundary, compares it with refined analytic torsion, and establishes a gluing formula under flat Hermitian metrics, advancing spectral geometry tools.

Contribution

It introduces the Cappell-Miller analytic torsion for manifolds with boundary and proves a new gluing formula in the flat metric case.

Findings

Extended torsion to manifolds with boundary

Compared Cappell-Miller and refined analytic torsion

Established gluing formula for flat Hermitian metrics

Abstract

Inspired by the work of Boris Vertman on refined analytic torsion for manifolds with boundary, in this paper we extend the construction of the Cappell-Miller analytic torsion to manifolds with boundary. We also compare it with the refined analytic torsion on manifolds with boundary. As a byproduct of the gluing formula for refined analytic torsion and the comparison theorem for the Cappell-Miller analytic torsion and the refined analytic torsion, we establish the gluing formula for the Cappell-Miller analytic torsion in the case that the Hermitian metric is flat.