By R. C. Penner
Measured geodesic laminations are a normal generalization of straightforward closed curves in surfaces, and so they play a decisive position in a number of advancements in two-and 3-dimensional topology, geometry, and dynamical structures. This ebook provides a self-contained and complete therapy of the wealthy combinatorial constitution of the gap of measured geodesic laminations in a hard and fast floor. households of measured geodesic laminations are defined by means of specifying a educate music within the floor, and the gap of measured geodesic laminations is analyzed by means of learning houses of teach tracks within the floor. the fabric is constructed from first ideas, the recommendations hired are basically combinatorial, and just a minimum heritage is needed at the a part of the reader. particularly, familiarity with basic differential topology and hyperbolic geometry is believed. the 1st bankruptcy treats the fundamental concept of educate tracks as chanced on by means of W. P. Thurston, together with recurrence, transverse recurrence, and the specific development of a measured geodesic lamination from a measured teach music. the following chapters enhance sure fabric from R. C. Penner's thesis, together with a common equivalence relation on measured educate tracks and conventional types for the equivalence periods (which are used to research the topology and geometry of the gap of measured geodesic laminations), a duality among transverse and tangential buildings on a teach song, and the specific computation of the motion of the mapping category crew at the area of measured geodesic laminations within the surface.
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