2017/01/31 by Dan Cristofaro-Gardiner, Michael Hutchings, Dan Pomerleano · 1 citation
Mathematics · #math.SG #math.DS #msc:53D10 #msc:37C27
paper · pdf · doi:10.2140/gt.2019.23.3601
published as Geom. Topol. 23 (2019) 3601-3645 · 42 pages, minor corrections and expository improvements
arxiv created 2018/06/23 · arxiv updated 2020/01/08
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 non-torsion contact structures, every nondegenerate contact form has at least four simple Reeb orbits.