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Branched surfaces in contact geometry

Abstract : The purpose of this thesis is to establish links between the theory of laminations and the theory of contact structures, via branched surfaces. This will is motivated by the existence of links between tight contact structures and taut foliations.
The main result is a sufficient condition for a branched surface B in a 3-dimensional manifold V to fully carry a lamination. It implies a sufficient condition for the lift of B in the universal cover of V to fully carry a lamination, which is also a necessary condition for this lamination to be essential. This result gives a piece of answer to a classical question of Gabai.
We then introduce a notion of contact structure carried by a branched surface, which generalizes the one of Oertel-Swiatkowski. At last, we give a sufficient condition for two contact structures to be carried, modulo isotopy, by the same branched surface.
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Contributor : Skander Zannad <>
Submitted on : Wednesday, October 4, 2006 - 4:36:33 PM
Last modification on : Monday, March 25, 2019 - 4:52:05 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 6:11:36 PM



  • HAL Id : tel-00103561, version 1



Skander Zannad. Branched surfaces in contact geometry. Mathématiques [math]. Université de Nantes, 2006. Français. ⟨tel-00103561⟩



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