Mathematics – Geometric Topology
Scientific paper
1998-09-18
Geom. Topol. Monogr. 2 (1999), 35-86
Mathematics
Geometric Topology
52 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon2/paper3.abs.html
Scientific paper
David Gabai showed that disk decomposable knot and link complements carry taut foliations of depth one. In an arbitrary sutured 3-manifold M, such foliations F, if they exist at all, are determined up to isotopy by an associated ray [F] issuing from the origin in H^1(M;R) and meeting points of the integer lattice H^1(M;Z). Here we show that there is a finite family of nonoverlapping, convex, polyhedral cones in H^1(M;R) such that the rays meeting integer lattice points in the interiors of these cones are exactly the rays [F]. In the irreducible case, each of these cones corresponds to a pseudo-Anosov flow and can be computed by a Markov matrix associated to the flow. Examples show that, in disk decomposable cases, these are effectively computable. Our result extends to depth one a well known theorem of Thurston for fibered 3-manifolds. The depth one theory applies to higher depth as well.
Cantwell John
Conlon Lawrence
No associations
LandOfFree
Foliation Cones does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Foliation Cones, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Foliation Cones will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-458463