Geometry & Topology

Contact structures, deformations and taut foliations

Jonathan Bowden

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Abstract

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.

Article information

Source
Geom. Topol., Volume 20, Number 2 (2016), 697-746.

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

Permanent link to this document
https://projecteuclid.org/euclid.gt/1510858969

Digital Object Identifier
doi:10.2140/gt.2016.20.697

Mathematical Reviews number (MathSciNet)
MR3493095

Zentralblatt MATH identifier
1338.53053

Subjects
Primary: 53C12: Foliations (differential geometric aspects) [See also 57R30, 57R32] 53D10: Contact manifolds, general
Secondary: 53C24: Rigidity results 37D20: Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)

Keywords
contact structure circle action taut foliation

Citation

Bowden, Jonathan. Contact structures, deformations and taut foliations. Geom. Topol. 20 (2016), no. 2, 697--746. doi:10.2140/gt.2016.20.697. https://projecteuclid.org/euclid.gt/1510858969


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