Download E-books Combinatorics of Train Tracks. (AM-125) (Annals of Mathematics Studies) PDF

By R. C. Penner

Measured geodesic laminations are a usual generalization of straightforward closed curves in surfaces, they usually play a decisive function in a variety of advancements in two-and 3-dimensional topology, geometry, and dynamical platforms. This booklet offers a self-contained and entire remedy of the wealthy combinatorial constitution of the distance of measured geodesic laminations in a set floor. households of measured geodesic laminations are defined via specifying a teach tune within the floor, and the gap of measured geodesic laminations is analyzed by means of learning houses of teach tracks within the floor. the cloth is constructed from first ideas, the recommendations hired are primarily combinatorial, and just a minimum heritage is needed at the a part of the reader. particularly, familiarity with common differential topology and hyperbolic geometry is thought. the 1st bankruptcy treats the elemental concept of teach tracks as chanced on by means of W. P. Thurston, together with recurrence, transverse recurrence, and the categorical development of a measured geodesic lamination from a measured educate music. the following chapters improve definite fabric from R. C. Penner's thesis, together with a typical equivalence relation on measured educate tracks and conventional types for the equivalence periods (which are used to research the topology and geometry of the distance of measured geodesic laminations), a duality among transverse and tangential constructions on a educate tune, and the categorical computation of the motion of the mapping type workforce at the house of measured geodesic laminations within the surface.

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