Communications in Analysis and Geometry

Volume 27 (2019)

Number 2

Taut foliations

Pages: 357 – 375

DOI: https://dx.doi.org/10.4310/CAG.2019.v27.n2.a4

Authors

Vincent Colin (Département de Mathématiques, Université de Nantes, France)

William H. Kazez (Department of Mathematics, University of Georgia, Athens, Ga., U.S.A.)

Rachel Roberts (Department of Mathematics, Washington University, St. Louis, Missouri, U.S.A.)

Abstract

We describe notions of tautness that arise in the study of $C^0$ foliations, $C^{1,0}$ or smoother foliations, and in geometry. We give examples to show that these notions are different. We prove that these variations of tautness are equivalent up to topological conjugacy, but their differences impact some classical foliation results. In particular, we construct examples of smoothly taut $C^{\infty, 0}$ foliations that can be $C^0$ approximated by both weakly symplectically fillable, universally tight contact structures and by overtwisted contact structures.

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Vincent Colin was supported in part by the ERC grant Geodycon and the ANR grant Quantact.

William H. Kazez was supported in part by grants from the Simons Foundation (#244855) and the National Science Foundation (DMS-1612036).

Rachel Roberts was supported in part by grants from the Simons Foundation (#317884) and the National Science Foundation (DMS-1612475).

Received 14 December 2016

Accepted 10 January 2017

Published 23 August 2019