Rachel Roberts

Infinitely many hyperbolic 3-manifolds which contain no Reebless foliation

Calegari [Ca] has shown that if M is also atoroidal, then or1(M) is Gromov negatively curved. Furthermore, Thurston has proposed an approach to demonstrating geometrization for such M. Many 3-manifolds contain Reebless foliations, and it has often been conjectured that all closed hyperbolic 3-manifolds do. (It is our impression that for many years Hatcher provided the sole voice of dissent.) In this paper, we give the first examples of closed hyperbolic 3-manifolds which contain no Reebless foliation.

Fractional Dehn twists in knot theory and contact topology

Fractional Dehn twists give a measure of the difference between the relative isotopy class of a homeomorphism of a bordered surface and the Thurston representative of its free isotopy class. We show how to estimate and compute these invariants. We discuss the the relationship of our work to stabilization problems in classical knot theory, general open book decompositions, and contact topology. We include an elementary characterization of overtwistedness for contact structures described by open book decompositions.

C0 approximations of foliations

Suppose that

TAUT FOLIATIONS IN KNOT COMPLEMENTS

\mathcal F

Group actions on order trees

is a transversely oriented, codimension one foliation of a connected, closed, oriented 3-manifold. Suppose also that

Taut foliations in surface bundles with multiple boundary components

\mathcal F

Taut foliations in punctured surface bundles, I

has continuous tangent plane field and is {\sl taut}; that is, closed smooth transversals to

Alternating knots satisfy strong property P

\mathcal F

Constructing taut foliations.

pass through every point of

When incompressible tori meet essential laminations

M