Combinatorics of Train Tracks. (AM-125), Volume 125
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A01=John L. Harer
A01=R. C. Penner
Ambient isotopy
Analytic function
Author_John L. Harer
Author_R. C. Penner
Brouwer fixed-point theorem
Cantor set
Category=PBV
Category=TRF
Combinatorics
Compactification (mathematics)
Conjugacy class
Connectivity (graph theory)
Cotangent space
CW complex
Deformation theory
Differential topology
Disjoint union
Disk (mathematics)
Eigenvalues and eigenvectors
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eq_isMigrated=1
eq_nobargain
eq_non-fiction
eq_tech-engineering
Equivalence class
Equivalence class (music)
Equivalence relation
Euler characteristic
Explicit formulae (L-function)
Foliation
Geodesic curvature
Geometry
Harmonic function
Homeomorphism
Homotopy
Horocycle
Hyperbolic geometry
Hyperbolic space
Incidence matrix
Inequality (mathematics)
Infimum and supremum
Intersection (set theory)
Intersection number
Intersection number (graph theory)
Interval (mathematics)
Invariance of domain
Invariant measure
Jordan curve theorem
Kähler manifold
Lexicographical order
Linear map
Linear subspace
Mapping class group
Mathematical induction
Natural topology
Orientability
Pair of pants (mathematics)
Parametrization
Parity (mathematics)
Projective space
Quadratic differential
Scientific notation
Sign (mathematics)
Special case
Support (mathematics)
Symplectic geometry
Symplectomorphism
Teichmüller space
Theorem
Topological space
Topology
Total order
Train track (mathematics)
Transitive relation
Transversality (mathematics)
Transverse measure
Uniformization theorem
Unit tangent bundle
Vector field
Product details
- ISBN 9780691025315
- Weight: 312g
- Dimensions: 152 x 235mm
- Publication Date: 23 Dec 1991
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
