On the existence of supporting broken book decompositions for contact forms in dimension 3

Abstract : We prove that in dimension 3 every nondegenerate contact form is carried by a broken book decomposition. As an application we get that if M is a closed irreducible oriented 3-manifold that is not a graph manifold, for example a hyperbolic manifold, then every nondegenerate Reeb vector field on M has positive topological entropy. Moreover, we obtain that on a closed 3-manifold, every nondegenerate Reeb vector field has either two or infinitely many periodic orbits, and two periodic orbits are possible only on the sphere or on a lens space.
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Submitted on : Thursday, February 6, 2020 - 9:12:03 AM
Last modification on : Friday, February 14, 2020 - 1:36:53 AM

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  • HAL Id : hal-02426945, version 2
  • ARXIV : 2001.01448

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Vincent Colin, Pierre Dehornoy, Ana Rechtman. On the existence of supporting broken book decompositions for contact forms in dimension 3. 2020. ⟨hal-02426945v2⟩

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