Analysis and PDE Seminar: Pollicott-Ruelle resonances and Betti numbers

Seminar | October 21 | 4:10-5 p.m. | 939 Evans Hall

 Benjamin Küster, Paris 11

 Department of Mathematics

In joint work with Tobias Weich, we study the multiplicity of the Pollicott-Ruelle resonance 0 of the Lie derivative along the geodesic vector field on the cosphere bundle of a closed negatively curved Riemannian manifold, acting on flow-transversal one-forms. We prove that if the manifold admits a metric of constant negative curvature and the Riemannian metric is close to such a constant curvature metric, then the considered resonance multiplicity agrees with the first Betti number of the manifold, provided the latter does not have dimension 3. In dimension 3 and for constant curvature, it turns out that the resonance multiplicity is twice the first Betti number.