Spectral diameter, Liouville domains and symplectic cohomology

Abstract: The spectral norm provides a lower bound to the Hofer norm. It is thus natural to ask whether the diameter of the spectral norm is finite or not. In the case of closed symplectic manifolds, there is no unified answer. For instance, for a certain class of symplecticaly aspherical manifolds, which contains surfaces, the spectral diameter is infinite. However, for CP^n, the spectral diameter is known to be finite. During this talk, I will prove that, in the case of Liouville domains, the spectral diameter is finite if and only if the symplectic cohomology of the underlying manifold vanishes. With that relationship in hand, we will explore applications to symplecticaly aspherical symplectic manifolds and give a new proof that the spectral diameter is infinite on cotangent disk bundles.

differential geometrydynamical systemsgeometric topologysymplectic geometryspectral theory

Audience: researchers in the topic

Geometry and Dynamics seminar

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