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2016 Contact structures, deformations and taut foliations
Jonathan Bowden
Geom. Topol. 20(2): 697-746 (2016). DOI: 10.2140/gt.2016.20.697


Using deformations of foliations to contact structures as well as rigidity properties of Anosov foliations we provide infinite families of examples which show that the space of taut foliations in a given homotopy class of plane fields need not be path connected. Similar methods also show that the space of representations of the fundamental group of a hyperbolic surface to the group of smooth diffeomorphisms of the circle with fixed Euler class is in general not path connected. As an important step along the way we resolve the question of which universally tight contact structures on Seifert fibred spaces are deformations of taut or Reebless foliations when the genus of the base is positive or the twisting number of the contact structure in the sense of Giroux is non-negative.


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Jonathan Bowden. "Contact structures, deformations and taut foliations." Geom. Topol. 20 (2) 697 - 746, 2016.


Received: 29 October 2013; Revised: 29 May 2015; Accepted: 28 June 2015; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1338.53053
MathSciNet: MR3493095
Digital Object Identifier: 10.2140/gt.2016.20.697

Primary: 53C12 , 53D10
Secondary: 37D20 , 53C24

Keywords: circle action , contact structure , taut foliation

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.20 • No. 2 • 2016
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