Train Track Lamination

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Train track lamination. If each vertical fiber has nontrivial intersection with some leaf then the lamination is fully carried by the train track. 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. Get it as soon as wed sep 2. Place your longest carriage on the outside track and lightly tack a pen to the centre of the coach.

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 of a 2 dimensional hyperbolic manifold is a closed subset together with a foliation of this closed subset by geodesics. Hearing and seeing this my big brother found us a pretty beaten up well loved brio train table as well as a good collection of track and trains on craigslist for 50. 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.

Take any of the amtrak train routes instead of flying to hot travel destinations. While the trains and track came into the house to be played with right away the table sat in the garage waiting for a makeover in time for santa clause to bring it on. If the lines do not meet then the rails are far enough apart. 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.

It s often more natural to look at measured laminations for example as we have seen in the older post measured laminations are natural generalizations of multi curves and the space is homeomorphic to thurston with very natural coordinate charts given by train tracks. Repeat with the pen fixed to one end of the same carriage now on the inside track. 69 8 85 piece 19 37 19 37. One application of the dictionary is to the study of thurston s classification of mapping classes on s cb88.

These are used in thurston s classification of elements of the mapping class group and in his theory of earthquake maps.