Analytic torsion on manifolds with fibred boundary metrics

TL;DR

This paper develops a method to compute the renormalized analytic torsion on manifolds with fibred boundary metrics by analyzing heat kernel asymptotics and applying renormalization techniques.

Contribution

It introduces a novel approach to construct the renormalized analytic torsion using heat kernel asymptotics on manifolds with fibred boundary metrics.

Findings

Derived asymptotics of heat kernel in short and long time regimes

Established a procedure for renormalizing the zeta function and determinant

Provided a framework for analytic torsion on fibred boundary manifolds

Abstract

In this paper, we construct the renormalized analytic torsion in the setup of manifold endowed with fibred boundary metrics. The method of construction is to determine the asymptotic of heat kernel, both in short time regime and long time regime and apply these asymptotics together with renormalization to determine the renormalized zeta function and the determinant of Hodge Laplacian.