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Combinatorics of Train Tracks (Annals of Mathematics Studies, 125) - Tapa dura

Libro 128 de 202: Annals of Mathematics Studies

Penner, R. C.; Harer, John L.

 
9780691087641: Combinatorics of Train Tracks (Annals of Mathematics Studies, 125)
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ISBN 10: 0691087644 ISBN 13: 9780691087641
Editorial: Princeton University Press, 1992

Sinopsis

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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Críticas

"The book is beautifully written, with a clear path of theoretical development amid a wealth of detail for the technician. . . . [T]his text provides a valuable reference work as well as a readable introduction for the student or newcomer to the area."--Zentralblatt fòr Mathematik

Reseña del editor


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 computation of the action of the mapping class group on the space of measured geodesic laminations in the surface.


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Editorial
Princeton University Press
Año de publicación
1992
Idioma
Inglés
ISBN 10 
0691087644
ISBN 13 
9780691087641
Encuadernación
Tapa dura
Número de páginas
232
Contacto del fabricante
no disponible
Persona responsable
no disponible