Combinatorics of train tracks / by R.C. Penner with J.L. Harer.
Material type: TextSeries: Annals of mathematics studiesPublication details: Princeton, N.J. : Princeton University Press, 1992.Description: xi, 216 p. : ill. ; 25 cmISBN:- 0691087644 (alk. paper) :
- QA649 .P38 1991
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Includes bibliographical references (p. 214-216).
Preface 1.1Train Tracks 1.2Multiple Curves and Dehn's Theorem 1.3Recurrence and Transverse Recurrence 1.4Genericity and Transverse Recurrence 1.5Trainpaths and Transverse Recurrence 1.6Laminations 1.7Measured Laminations 1.8Bounded Surfaces and Tracks with Stops Ch. 2Combinatorial Equivalence 2.1Splitting, Shifting, and Carrying 2.2Equivalence of Birecurrent Train Tracks 2.3Splitting versus Shifting 2.4Equivalence versus Carrying 2.5Splitting and Efficiency 2.6The Standard Models 2.7Existence of the Standard Models 2.8Uniqueness of the Standard Models Ch. 3The Structure of ML[subscript 0] 3.1The Topology of ML[subscript 0] and PL[subscript 0] 3.2The Symplectic Structure of ML[subscript 0] 3.3Topological Equivalence 3.4Duality and Tangential Coordinates Epilogue Addendum The Action of Mapping Classes on ML[subscript 0] Bibliography
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 treatment of the 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.
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