Variation of the analytic torsion of the perturbed Laplace operator on a manifold with boundary.

30.11.2023, 16:00  –  Haus 9, Raum 0.14
Forschungsseminar Differentialgeometrie

Ihsane Malass

Ray and Singer proved that on a closed manifold the analytic torsion is independent of the choice of Riemannian metric and on a compact manifold with boundary under relative / absolute boundary conditions, it depends only on the metric on the boundary. Mathai and Wu considered a perturbed Laplace operator by a closed form on a closed, and proved that the resulting analytic torsion remains independent of the choice of the metric. We extend their construction to the case of a compact manifold with boundary under proper boundary conditions. We aim to prove, using Hilbert space methods and Heat kernel analysis, that it remains independent of the metric on the interior of the manifold, and depend solely on the expression of the metric near the boundary.  We give an overview of the proof and investigate some future questions.