Lower complexity bounds for positive contactomorphisms

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Abstract

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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© Hebrew University of Jerusalem 2018

Authors and Affiliations

  1. 1.Institut de MathématiquesUniversité de Neuchâtel (UNINE)NeuchâtelSwitzerland

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