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

Penner, Rc

Hardcover

ISBN 10: 0691087644 ISBN 13: 9780691087641

Publisher: Princeton University Press, 1992

Synopsis

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.

About this title

Review

"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

From the Back Cover

We study here one aspect of the mathematics pioneered by William P. Thurston, namely, the rich combinatorial structure of the space of measured geodesic laminations in a fixed surface. Roughly, a train track is a CW complex in the surface (together with extra structure), and appropriate train tracks correspond to charts on this manifold.

Edition details

• Publisher: Princeton University Press
• Publication date: 1992
• Language: English
• ISBN 10: 0691087644
• ISBN 13: 9780691087641
• Binding: Hardcover
• Number of pages: 232