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

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

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 co...

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Superior document:Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
VerfasserIn:
Penner, R. C.,
Harer, John L.,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2016]
©1992
Year of Publication:2016
Language:English
Series:Annals of Mathematics Studies ; 125
Online Access:
Physical Description:1 online resource (232 p.)
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100 1 |a Penner, R. C.,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a Combinatorics of Train Tracks. (AM-125), Volume 125 /  |c R. C. Penner, John L. Harer. 
264 1 |a Princeton, NJ :   |b Princeton University Press,   |c [2016] 
264 4 |c ©1992 
300 |a 1 online resource (232 p.) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
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490 0 |a Annals of Mathematics Studies ;  |v 125 
505 0 0 |t Frontmatter --   |t Contents --   |t Preface --   |t Acknowledgements --   |t Chapter 1. The Basic Theor --   |t Chapter 2. Combinatorial Equivalence --   |t Chapter 3. The Structure of ML0 --   |t Epilogue --   |t Addendum. The Action of Mapping Classes on ML0 --   |t Bibliography 
506 0 |a restricted access  |u http://purl.org/coar/access_right/c_16ec  |f online access with authorization  |2 star 
520 |a 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. 
530 |a Issued also in print. 
538 |a Mode of access: Internet via World Wide Web. 
546 |a In English. 
588 0 |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) 
650 0 |a CW complexes. 
650 0 |a Combinatorial analysis. 
650 0 |a Geodesics (Mathematics). 
650 7 |a MATHEMATICS / Combinatorics.  |2 bisacsh 
653 |a Ambient isotopy. 
653 |a Analytic function. 
653 |a Axiom. 
653 |a Brouwer fixed-point theorem. 
653 |a CW complex. 
653 |a Cantor set. 
653 |a Cardinality. 
653 |a Change of basis. 
653 |a Coefficient. 
653 |a Combinatorics. 
653 |a Compactification (mathematics). 
653 |a Conjugacy class. 
653 |a Connected component (graph theory). 
653 |a Connectivity (graph theory). 
653 |a Coordinate system. 
653 |a Cotangent space. 
653 |a Covering space. 
653 |a Deformation theory. 
653 |a Dehn twist. 
653 |a Diffeomorphism. 
653 |a Differential topology. 
653 |a Disjoint sets. 
653 |a Disjoint union. 
653 |a Disk (mathematics). 
653 |a Eigenvalues and eigenvectors. 
653 |a Embedding. 
653 |a Equation. 
653 |a Equivalence class (music). 
653 |a Equivalence class. 
653 |a Equivalence relation. 
653 |a Euclidean space. 
653 |a Euler characteristic. 
653 |a Explicit formula. 
653 |a Explicit formulae (L-function). 
653 |a Fiber bundle. 
653 |a Foliation. 
653 |a Fuchsian group. 
653 |a Geodesic curvature. 
653 |a Geometry. 
653 |a Harmonic function. 
653 |a Homeomorphism. 
653 |a Homotopy. 
653 |a Horocycle. 
653 |a Hyperbolic geometry. 
653 |a Hyperbolic motion. 
653 |a Hyperbolic space. 
653 |a Incidence matrix. 
653 |a Inequality (mathematics). 
653 |a Infimum and supremum. 
653 |a Injective function. 
653 |a Intersection (set theory). 
653 |a Intersection number (graph theory). 
653 |a Intersection number. 
653 |a Interval (mathematics). 
653 |a Invariance of domain. 
653 |a Invariant measure. 
653 |a Jordan curve theorem. 
653 |a Kähler manifold. 
653 |a Lexicographical order. 
653 |a Linear map. 
653 |a Linear subspace. 
653 |a Mapping class group. 
653 |a Mathematical induction. 
653 |a Monogon. 
653 |a Natural topology. 
653 |a Orientability. 
653 |a Pair of pants (mathematics). 
653 |a Parallel curve. 
653 |a Parametrization. 
653 |a Parity (mathematics). 
653 |a Projective space. 
653 |a Quadratic differential. 
653 |a Scientific notation. 
653 |a Sign (mathematics). 
653 |a Special case. 
653 |a Spectral radius. 
653 |a Standard basis. 
653 |a Subsequence. 
653 |a Subset. 
653 |a Summation. 
653 |a Support (mathematics). 
653 |a Symplectic geometry. 
653 |a Symplectomorphism. 
653 |a Tangent space. 
653 |a Tangent vector. 
653 |a Tangent. 
653 |a Teichmüller space. 
653 |a Theorem. 
653 |a Topological space. 
653 |a Topology. 
653 |a Total order. 
653 |a Train track (mathematics). 
653 |a Transitive relation. 
653 |a Transpose. 
653 |a Transversality (mathematics). 
653 |a Transverse measure. 
653 |a Uniformization theorem. 
653 |a Unit tangent bundle. 
653 |a Unit vector. 
653 |a Vector field. 
700 1 |a Harer, John L.,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
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773 0 8 |i Title is part of eBook package:  |d De Gruyter  |t Princeton University Press eBook-Package Archive 1927-1999  |z 9783110442496 
776 0 |c print  |z 9780691025315 
856 4 0 |u https://doi.org/10.1515/9781400882458 
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856 4 2 |3 Cover  |u https://www.degruyter.com/document/cover/isbn/9781400882458/original 
912 |a 978-3-11-044249-6 Princeton University Press eBook-Package Archive 1927-1999  |c 1927  |d 1999 
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