Train Track Lamination

If a generic lamination on a surface is looked at from a distance by a myopic person it will look like a train track.

Train track lamination.

The weights vary over a convex cone and these cones give coordinate charts for a manifold. The maximum euler characteristic function is continuous on certain parametrized families of lamination links carried by a train track neighborhood. 21 november 2006 original upload date source. The pil structure on the space of measured geodesic laminations.

S g n s g n homotopic to the identity mapping into and such. Iwip automorphism outer automorphism train track lamination self a ne tiling rauzy fractal substitution word combinatorics substitutive dynamical system graph directed iterated function system pisot number discrete spectrum. Introduction symbolic dynamical systems were rst introduced more than a century ago to gain insight. A lamination of a surface is a partition of a closed subset of the surface into smooth curves.

If each vertical fiber has nontrivial intersection with some leaf then the lamination is fully carried by the train track. A switch in a train track and the corresponding portion of a lamination. David eppstein at english wikipedia. One of maximum euler characteristic subject to the condition that the seifert lamination is carried by an aspherical branched surface and satisfying fur ther conditions.

Via train tracks. The second task for this puzzle is to mark all the implied cells. These are cells where there is a piece of track that points to that cell. Given a train track in m satisfying certain nontriviality condi tions then each assignment of positive weights to the various sectors of subject to compatibility conditions at the branching loci deflnes a measured lamination.

A train track is said to carry a lamination if there is a train track neighborhood such that every leaf of the lamination is contained in the neighborhood and intersects each vertical fiber transversely. Every train track can be turned into a generic train track by sliding its edges. Transferred from to commons. When one considers the teichmüller space t x of the riemann surface x it is natural to restrict the attention to the space ml b x of bounded measured laminations.

A geodesic lamination on s g n is said to be carried by a train track if there is a di eren tiable map f. One can also use train track expansions to detect finer properties of a measured lamination such as arationality which means that the lami nation fills the whole surface. Furthermore we show that the weak topology on the measured laminations weakly carried by a train track corresponds to a pointwise weak convergence of the edge weight systems.