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Annali di Matematica Pura ed Applicata

, Volume 178, Issue 1, pp 81–102 | Cite as

Branched spines and contact structures on 3-manifolds

  • Riccardo Benedetti
  • Carlo Petronio
Article

Abstract

We introduce and analyze the characteristic foliation induced by a contact structure on a branched surface, in particular a branched standard spine of a 3-manifold. We extend to (fairly general) singular foliations of branched surfaces the local existence and uniqueness results which hold for genuine surfaces. Moreover we show that global uniqueness holds when restricting to tight structures. We establish branched versions of the elimination lemma. We prove a smooth version of the Gillman-Rolfsen PL-embedding theorem, deducing that branched spines can be used to construct contact structures in a given homotopy class of plane fields.

Mathematics Subject Classification (1991)

57N10 (primary) 57R15 57R25 (secondary) 

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Copyright information

© Fondazione Annali di Matematica Pure ed Applicata 2000

Authors and Affiliations

  • Riccardo Benedetti
    • 1
  • Carlo Petronio
    • 1
  1. 1.Dipartimento di MatematicaUniversità di PisaPisaItaly

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