English

On the structure of Besse convex contact spheres

Symplectic Geometry 2023-02-24 v2 Algebraic Topology Differential Geometry

Abstract

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

Keywords

Cite

@article{arxiv.2012.05389,
  title  = {On the structure of Besse convex contact spheres},
  author = {Marco Mazzucchelli and Marco Radeschi},
  journal= {arXiv preprint arXiv:2012.05389},
  year   = {2023}
}

Comments

29 pages; final version: we added a reference to Ustilovsky's construction of exotic Besse contact spheres. To appear in Trans. Amer. Math. Soc