Approximating C1,0C^{1,0}-foliations

We extend the Eliashberg-Thurston theorem on approximations of taut oriented $C^2$-foliations of 3-manifolds by both positive and negative contact structures to a large class of taut oriented $C^{1,0}$-foliations, where by $C^{1,0}$ foliation, we mean a foliation with continuous tangent plane field. These $C^{1,0}$-foliations can therefore be approximated by weakly symplectically fillable, universally tight, contact structures. This allows applications of $C^2$-foliation theory to contact topology and Floer theory to be generalized and extended to constructions of $C^{1,0}$-foliations.Comment: 52 pages, 5 figures. Final version with updated references, corrections and terminolog

Group negative curvature for 3-manifolds with genuine laminations

We show that if a closed atoroidal 3-manifold M contains a genuine lamination, then it is group negatively curved in the sense of Gromov. Specifically, we exploit the structure of the non-product complementary regions of the genuine lamination and then apply the first author's Ubiquity Theorem to show that M satisfies a linear isoperimetric inequality.Comment: 13 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol2/paper4.abs.htm

A TRAILER, A SHOTGUN, AND A THEOREM OF PYTHAGORAS

Counselor: Please tell the Court your name. Expert Witness: My name is Will Kazez Counselor: No, no, no! Your name is… This is not a good start. I am not naturally a nervous person. I have survived teaching calculus to a large class that included the entire freshman football team of the University of Pennsylvania, but I\u27ve never been an Expert Witness. Even though I\u27m confident of the mathematics, I\u27m not sure I like the idea of being cross-examined. But still, I\u27m just rehearsing my testimony with the lawyer, and even if I\u27ve got my own name a little wrong, what\u27s the worry? At any rate, lawyers do not like being interrupted