Combinatorics of Train Tracks. (AM-125)
( Annals of Mathematics Studies )
Publication series ：Annals of Mathematics Studies
Author： Penner R. C.;Harer John L.
Publisher： Princeton University Press
Publication year： 2016
E-ISBN: 9781400882458
P-ISBN(Paperback): 9780691025315
Subject： O157.1 portfolio analysis
Keyword： 拓扑（形势几何学）,数学,高等数学
Language： ENG
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
Description
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 laminations 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 computatio
Chapter