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Combinatorics of Train Tracks. (AM-125)
R. C. Penner and John L. Harer

Book Description | Reviews

TABLE OF CONTENTS:

Preface
Acknowledgements
Ch. 1The Basic Theory3
1.1Train Tracks4
1.2Multiple Curves and Dehn's Theorem10
1.3Recurrence and Transverse Recurrence18
1.4Genericity and Transverse Recurrence39
1.5Trainpaths and Transverse Recurrence60
1.6Laminations68
1.7Measured Laminations82
1.8Bounded Surfaces and Tracks with Stops102
Ch. 2Combinatorial Equivalence115
2.1Splitting, Shifting, and Carrying116
2.2Equivalence of Birecurrent Train Tracks124
2.3Splitting versus Shifting127
2.4Equivalence versus Carrying133
2.5Splitting and Efficiency139
2.6The Standard Models145
2.7Existence of the Standard Models154
2.8Uniqueness of the Standard Models160
Ch. 3The Structure of ML[subscript 0]173
3.1The Topology of ML[subscript 0] and PL[subscript 0]174
3.2The Symplectic Structure of ML[subscript 0]182
3.3Topological Equivalence188
3.4Duality and Tangential Coordinates191
Epilogue204
Addendum The Action of Mapping Classes on ML[subscript 0]210
Bibliography214

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File created: 8/26/2014

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