On the structure of Besse convex contact spheres

Marco Mazzucchelli (1) , Marco Radeschi (2)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
2 UND - University of Notre Dame [Indiana]

We consider convex contact spheres $Y$ all of whose Reeb orbits are closed. Any such $Y$ admits a stratification by the periods of closed Reeb orbits. We show that $Y$ "resembles" a contact ellipsoid: any stratum of $Y$ is an integral homology sphere, and the sequence of Ekeland-Hofer spectral invariants of $Y$ coincides with the full sequence of action values, each one repeated according to its multiplicity.

Domaines: Géométrie symplectique [math.SG]; Topologie algébrique [math.AT]; Géométrie différentielle [math.DG]

Marco Mazzucchelli, Marco Radeschi. On the structure of Besse convex contact spheres. Transactions of the American Mathematical Society, 2023, 376 (3), pp.2125-2153. ⟨10.1090/tran/8836⟩. ⟨ensl-03053467⟩