Torsion contact forms in three dimensions have two or infinitely many Reeb orbits

Cristofaro-Gardiner, Dan¹ ; Hutchings, Michael² ; Pomerleano, Daniel³

¹ Mathematics Department, University of California, Santa Cruz, Santa Cruz, CA, United States
² Mathematics Department, University of California, Berkeley, Berkeley, CA, United States
³ Mathematics Department, University of Massachusetts, Boston, Boston, MA, United States

Geometry & topology, Tome 23 (2019) no. 7, pp. 3601-3645.

Résumé

We prove that every nondegenerate contact form on a closed connected three-manifold such that the associated contact structure has torsion first Chern class has either two or infinitely many simple Reeb orbits. By previous results it follows that under the above assumptions, there are infinitely many simple Reeb orbits if the three-manifold is not the three-sphere or a lens space. We also show that for nontorsion contact structures, every nondegenerate contact form has at least four simple Reeb orbits.

Détail

DOI : 10.2140/gt.2019.23.3601

Classification : 53D10, 53D42
Keywords: Reeb dynamics, Weinstein conjecture, embedded contact homology

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