Lower complexity bounds for positive contactomorphisms
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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.
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