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$C^0$ approximations of foliations

William H Kazez and Rachel Roberts

Geometry & Topology 21 (2017) 3601–3657

Suppose that is a transversely oriented, codimension-one foliation of a connected, closed, oriented 3–manifold. Suppose also that has continuous tangent plane field and is taut; that is, closed smooth transversals to pass through every point of M. We show that if is not the product foliation S1 × S2, then can be C0 approximated by weakly symplectically fillable, universally tight contact structures. This extends work of Eliashberg and Thurston on approximations of taut, transversely oriented C2 foliations to the class of foliations that often arise in branched surface constructions of foliations. This allows applications of contact topology and Floer theory beyond the category of C2 foliated spaces.

taut foliation, holonomy, contact topology, weakly symplectically fillable, universally tight
Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 53D10
Received: 3 January 2016
Accepted: 30 January 2017
Published: 31 August 2017
Proposed: Cameron Gordon
Seconded: Yasha Eliashberg, András I Stipsicz
William H Kazez
Department of Mathematics
University of Georgia
Athens, GA
United States
Rachel Roberts
Department of Mathematics
Washington University
St Louis, MO
United States