Lower complexity bounds for positive contactomorphisms
- 13 Downloads
Let S*Q be the spherization of a closed connected manifold of dimension at least two. Consider a contactomorphism φ that can be reached by a contact isotopy that is everywhere positively transverse to the contact structure. In other words, φ is the time-1-map of a time-dependent Reeb flow. We show that the volume growth of φ is bounded from below by the topological complexity of the loop space of Q. Denote by ΩQ0(q) the component of the based loop space that contains the constant loop.
Unable to display preview. Download preview PDF.