Analytic torsion on manifolds with fibred boundary metrics

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.