Penner / Harer Combinatorics of Train Tracks. (AM-125), Volume 125

1. Auflage 2016
ISBN: 978-1-4008-8245-8
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, Band 125, 232 Seiten

Reihe: Annals of Mathematics Studies

No detailed description available for "Combinatorics of Train Tracks. (AM-125), Volume 125".

Autoren/Hrsg.

Penner, R. C.

Harer, John L.

Fachgebiete

• Mathematik | Informatik Mathematik Topologie
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik

Inhaltsverzeichnis

Preface

Acknowledgements

Ch. 1 The Basic Theory 3

1.1 Train Tracks 4

1.2 Multiple Curves and Dehn's Theorem 10

1.3 Recurrence and Transverse Recurrence 18

1.4 Genericity and Transverse Recurrence 39

1.5 Trainpaths and Transverse Recurrence 60

1.6 Laminations 68

1.7 Measured Laminations 82

1.8 Bounded Surfaces and Tracks with Stops 102

Ch. 2 Combinatorial Equivalence 115

2.1 Splitting, Shifting, and Carrying 116

2.2 Equivalence of Birecurrent Train Tracks 124

2.3 Splitting versus Shifting 127

2.4 Equivalence versus Carrying 133

2.5 Splitting and Efficiency 139

2.6 The Standard Models 145

2.7 Existence of the Standard Models 154

2.8 Uniqueness of the Standard Models 160

Ch. 3 The Structure of ML[subscript 0] 173

3.1 The Topology of ML[subscript 0] and PL[subscript 0] 174

3.2 The Symplectic Structure of ML[subscript 0] 182

3.3 Topological Equivalence 188

3.4 Duality and Tangential Coordinates 191

Epilogue 204

Addendum The Action of Mapping Classes on ML[subscript 0] 210

Bibliography 214