We discuss a link between the geometry of hyperbolic three-manifolds and their Floer theoretic invariants, provided by spectral geometry. In particular, we provide sufficient conditions for a hyperbolic three-manifold to be an L-space (i.e. the Floer homology group has the least possible rank) in terms of its volume and the geodesic spectrum (i.e. the set of lengths of closed geodesics). We discuss several explicit (numerical) examples in which this criterion can be applied. This is joint work in progress with Michael Lipnowski.
On the Floer homology and spectral geometry of hyperbolic three-manifolds
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Nom de l'orateur
Francesco Lin
Etablissement de l'orateur
Princeton
Date et heure de l'exposé
Lieu de l'exposé
Salle Eole