THE ZETA-DETERMINANTS AND ANALYTIC TORSION OF A METRIC MAPPING TORUS

초록

We use the BFK-gluing formula for zeta-determinants to compute the zetadeterminant and analytic torsion of a metric mapping torus induced from an isometry. As applications, we compute the zeta-determinants of the Laplacians defined on a Klein bottle K and some compact co-Kahler manifold T-phi. We also show that a metric mapping torus and a Riemannian product manifold with a round circle have the same heat trace asymptotic expansions. We finally compute the analytic torsion of a metric mapping torus for the Witten deformed Laplacian and recover the result of J. Marcsik in [16].

키워드