Approximating C0-foliations by contact structures

By Jonathan Bowden. 2015

64 citations recorded by the source corpus.

We show that any co-orientable foliation of dimension two on a closed orientable 3-manifold with continuous tangent plane field can be C0-approximated by both positive and negative contact structures unless all leaves of the foliation are simply connected. As applications we deduce that the existence of a taut C0-foliation implies the existence of universally tight contact structures in the same homotopy class of plane fields and that a closed 3-manifold that admits a taut C0-foliation of codimension-1 is not an L-space in the sense of Heegaard-Floer homology.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/035624b1fcd465619373d4c2709147e8da689132

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

$C^0$ Approximations of foliations (2015, methodology): “ion are planes. Throughout the paper, plane is used in the topological sense; that is, a plane is a surface homeomorphic to R2. We use Ito mean nondegenerate closed interval in places, and to mean I= [0;1] in other places, and the meaning should be clear from context. In Section 9 we brie y recall t”
Foliations, orders, representations, L-spaces and graph manifolds (2014, background): “ned with the Eliashberg-Thurston result to produce the appropriate contact structures, even though the foliations do not necessarily glue together to form a smooth foliation on W. Alternately, Bowden [Bn] and Kazez and Roberts [KR] have extended the Steven Boyer was partially supported by NSERC gran”
Floer simple manifolds and L-space intervals (2015, unknown): “In the late 1990’s, Eliashberg and Thurston [13] proved that one can associate a weakly symplectically fillable contact structure to any C2 cooriented taut foliation on a closed three-manifold—a result which Kazez and Roberts [29], and independently Bowden [5], have recently extended to C0 foliation”