Description
Book SynopsisMeasured 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 treatment of the combinatorial structure of the space of measured geodesic laminations in a fixed surface.
Trade 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 for Mathematik
Table of ContentsPrefaceAcknowledgementsCh. 1The Basic Theory31.1Train Tracks41.2Multiple Curves and Dehn's Theorem101.3Recurrence and Transverse Recurrence181.4Genericity and Transverse Recurrence391.5Trainpaths and Transverse Recurrence601.6Laminations681.7Measured Laminations821.8Bounded Surfaces and Tracks with Stops102Ch. 2Combinatorial Equivalence1152.1Splitting, Shifting, and Carrying1162.2Equivalence of Birecurrent Train Tracks1242.3Splitting versus Shifting1272.4Equivalence versus Carrying1332.5Splitting and Efficiency1392.6The Standard Models1452.7Existence of the Standard Models1542.8Uniqueness of the Standard Models160Ch. 3The Structure of ML[subscript 0]1733.1The Topology of ML[subscript 0] and PL[subscript 0]1743.2The Symplectic Structure of ML[subscript 0]1823.3Topological Equivalence1883.4Duality and Tangential Coordinates191Epilogue204Addendum The Action of Mapping Classes on ML[subscript 0]210Bibliography214
