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024 7 $a10.1515/9781400882458
035   $a(CKB)3710000000631324
035   $a(MiAaPQ)EBC4738728
035   $a(DE-B1597)467953
035   $a(OCoLC)979970579
035   $a(DE-B1597)9781400882458
035   $a(EXLCZ)993710000000631324
100   $a20190708d2016      fg 
101 0 $aeng
135   $aurcnu||||||||
181   $2rdacontent
182   $2rdamedia
183   $2rdacarrier
200 10$aCombinatorics of Train Tracks. (AM-125), Volume 125 /$fR. C. Penner, John L. Harer
210  1$aPrinceton, NJ :$cPrinceton University Press,$d[2016]
210  4$d©1992
215   $a1 online resource (233 pages) $cillustrations
225 1 $aAnnals of Mathematics Studies ;$v125
311   $a0-691-08764-4 
311   $a0-691-02531-2 
320   $aIncludes bibliographical references.
327   $tFrontmatter --$tContents --$tPreface --$tAcknowledgements --$tChapter 1. The Basic Theor --$tChapter 2. Combinatorial Equivalence --$tChapter 3. The Structure of ML0 --$tEpilogue --$tAddendum. The Action of Mapping Classes on ML0 --$tBibliography
330   $aMeasured geodesic laminations are a natural generalization of simple closed curves in surfaces, and they play a decisive role in various developments in two-and three-dimensional topology, geometry, and dynamical systems. This book presents a self-contained and comprehensive treatment of the rich combinatorial structure of the space of measured geodesic laminations in a fixed surface. Families of measured geodesic laminations are described by specifying a train track in the surface, and the space of measured geodesic laminations is analyzed by studying properties of train tracks in the surface. The material is developed from first principles, the techniques employed are essentially combinatorial, and only a minimal background is required on the part of the reader. Specifically, familiarity with elementary differential topology and hyperbolic geometry is assumed. The first chapter treats the basic theory of train tracks as discovered by W. P. Thurston, including recurrence, transverse recurrence, and the explicit construction of a measured geodesic lamination from a measured train track. The subsequent chapters develop certain material from R. C. Penner's thesis, including a natural equivalence relation on measured train tracks and standard models for the equivalence classes (which are used to analyze the topology and geometry of the space of measured geodesic laminations), a duality between transverse and tangential structures on a train track, and the explicit computation of the action of the mapping class group on the space of measured geodesic laminations in the surface.
410  0$aAnnals of mathematics studies ;$vno. 125.
606   $aGeodesics (Mathematics)
606   $aCW complexes
606   $aCombinatorial analysis
610   $aAmbient isotopy.
610   $aAnalytic function.
610   $aAxiom.
610   $aBrouwer fixed-point theorem.
610   $aCW complex.
610   $aCantor set.
610   $aCardinality.
610   $aChange of basis.
610   $aCoefficient.
610   $aCombinatorics.
610   $aCompactification (mathematics).
610   $aConjugacy class.
610   $aConnected component (graph theory).
610   $aConnectivity (graph theory).
610   $aCoordinate system.
610   $aCotangent space.
610   $aCovering space.
610   $aDeformation theory.
610   $aDehn twist.
610   $aDiffeomorphism.
610   $aDifferential topology.
610   $aDisjoint sets.
610   $aDisjoint union.
610   $aDisk (mathematics).
610   $aEigenvalues and eigenvectors.
610   $aEmbedding.
610   $aEquation.
610   $aEquivalence class (music).
610   $aEquivalence class.
610   $aEquivalence relation.
610   $aEuclidean space.
610   $aEuler characteristic.
610   $aExplicit formula.
610   $aExplicit formulae (L-function).
610   $aFiber bundle.
610   $aFoliation.
610   $aFuchsian group.
610   $aGeodesic curvature.
610   $aGeometry.
610   $aHarmonic function.
610   $aHomeomorphism.
610   $aHomotopy.
610   $aHorocycle.
610   $aHyperbolic geometry.
610   $aHyperbolic motion.
610   $aHyperbolic space.
610   $aIncidence matrix.
610   $aInequality (mathematics).
610   $aInfimum and supremum.
610   $aInjective function.
610   $aIntersection (set theory).
610   $aIntersection number (graph theory).
610   $aIntersection number.
610   $aInterval (mathematics).
610   $aInvariance of domain.
610   $aInvariant measure.
610   $aJordan curve theorem.
610   $aKähler manifold.
610   $aLexicographical order.
610   $aLinear map.
610   $aLinear subspace.
610   $aMapping class group.
610   $aMathematical induction.
610   $aMonogon.
610   $aNatural topology.
610   $aOrientability.
610   $aPair of pants (mathematics).
610   $aParallel curve.
610   $aParametrization.
610   $aParity (mathematics).
610   $aProjective space.
610   $aQuadratic differential.
610   $aScientific notation.
610   $aSign (mathematics).
610   $aSpecial case.
610   $aSpectral radius.
610   $aStandard basis.
610   $aSubsequence.
610   $aSubset.
610   $aSummation.
610   $aSupport (mathematics).
610   $aSymplectic geometry.
610   $aSymplectomorphism.
610   $aTangent space.
610   $aTangent vector.
610   $aTangent.
610   $aTeichmüller space.
610   $aTheorem.
610   $aTopological space.
610   $aTopology.
610   $aTotal order.
610   $aTrain track (mathematics).
610   $aTransitive relation.
610   $aTranspose.
610   $aTransversality (mathematics).
610   $aTransverse measure.
610   $aUniformization theorem.
610   $aUnit tangent bundle.
610   $aUnit vector.
610   $aVector field.
615  0$aGeodesics (Mathematics)
615  0$aCW complexes.
615  0$aCombinatorial analysis.
676   $a511/.6
686   $aSI 830$2rvk
700   $aPenner$b R. C.$0606391
702   $aHarer$b John L.
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910154745603321
996   $aCombinatorics of Train Tracks. (AM-125), Volume 125$92788030
997   $aUNINA