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Combinatorics of Train Tracks

Author: 


ISBN-13: 

9780691025315


ISBN: 

0691025312


Publisher:  Princeton University Press
Summary: Measured geodesic laminations are a natural generalization of simple closed curves in surfaces, and they play a decisive role in various developments in two-and three-dimensional topology, geometry, and dynamical systems. This book presents a self-contained and comprehensive treatment of the rich combinatorial structure of the space of measured geodesic laminations in a fixed surface. Families of measured geodesic la...minations are described by specifying a train track in the surface, and the space of measured geodesic laminations is analyzed by studying properties of train tracks in the surface. The material is developed from first principles, the techniques employed are essentially combinatorial, and only a minimal background is required on the part of the reader. Specifically, familiarity with elementary differential topology and hyperbolic geometry is assumed. The first chapter treats the basic theory of train tracks as discovered by W. P. Thurston, including recurrence, transverse recurrence, and the explicit construction of a measured geodesic lamination from a measured train track. The subsequent chapters develop certain material from R. C. Penner's thesis, including a natural equivalence relation on measured train tracks and standard models for the equivalence classes (which are used to analyze the topology and geometry of the space of measured geodesic laminations), a duality between transverse and tangential structures on a train track, and the explicit computation of the action of the mapping class group on the space of measured geodesic laminations in the surface.

Penner, R. C. is the author of Combinatorics of Train Tracks, published under ISBN 9780691025315 and 0691025312. Five hundred seventy five Combinatorics of Train Tracks textbooks are available for sale on ValoreBooks.com, one hundred ten used from the cheapest price of $14.50, or buy new starting at $20.00.
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Combinatorics of Train Tracks

ISBN-13: 9780691025315


ISBN: 0691025312


Publisher: Princeton University Press
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