Contact structures, deformations and taut foliations

Bowden, Jonathan

doi:10.2140/gt.2016.20.697

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Contact structures, deformations and taut foliations

Jonathan Bowden

Geometry & Topology 20 (2016) 697–746

DOI: 10.2140/gt.2016.20.697

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.

Keywords

contact structure, circle action, taut foliation

Mathematical Subject Classification 2010

Primary: 53C12, 53D10

Secondary: 53C24, 37D20

References

Publication

Received: 29 October 2013

Revised: 29 May 2015

Accepted: 28 June 2015

Published: 28 April 2016

Proposed: Yasha Eliashberg

Seconded: Benson Farb, Leonid Polterovich

Authors

Jonathan Bowden
Mathematisches Institut Ludwig-Maximillians-Universität Theresienstr. 39 D-80333 Munich Germany

Volume 20, issue 2 (2016)