算法拓扑学及三维流形的分类

图书标准信息

• 作者 [俄罗斯]马特维耶夫（Sergei Matveev） 著
• 出版社 科学出版社
• 出版时间 2011-06
• 版次 1
• ISBN 9787030313782
• 定价 98.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 492页
• 字数 630千字
• 正文语种 英语
• 丛书 国外数学名著系列

【内容简介】

《算法拓扑学及三维流形的分类》提供了一个全面、详细的3-维流形的分类并介绍了算法拓扑学，该书的作者也是这方面领域的专家。该书是springer的AlgorithmsandComputationinMathematics丛书的第九本。属于"反映学术前沿进展的优秀学术著作"这一类。

【目录】

SimpleandSpecialPolyhedra
1.1Spinesof3-Manifolds
1.1.1Collapsing
1.1.2Spines
1.1.3SimpleandSpecialPolyhedra
1.1.4SpecialSpines
1.1.5SpecialPolyhedraandSingularTriangulations
1.2ElementaryMovesonSpecialSpines~
1.2.1MovesonSimplePolyhedra
1.2.22-CellReplacementLemma
1.2.3BubbleMove
1.2.4MarkedPolyhedra
1.3SpecialPolyhedraWhicharenotSpines
1.3.1VariousNotionsofEquivalenceforPolyhedra
1.3.2MovesonAbstractSimplePolyhedra
1.3.3HowtoHittheTargetWithoutInverseU-Turns
1.3.4Zeeman'sCollapsingConjecture
ComplexityTheoryof3-Manifolds

2.1WhatistheComplexityofa3-Manifold?
2.1.1AlmostSimplePolyhedra
2.1.2DefinitionandEstimationoftheComplexity
2.2PropertiesofComplexity
2.2.1ConvertingAlmostSimpleSpinesintoSpecialOnes..
2.2.2TheFinitenessProperty
2.2.3TheAdditivityProperty
2.3ClosedManifoldsofSmallComplexity
2.3.1EnumerationProcedure
2.3.2SimplificationMoves
2.3.3ManifoldsofComplexity<6
Contents
2.4GraphManifoldsofWaldhausen
2.4.1PropertiesofGraphManifolds
2.4.2ManifoldsofComplexity<_8
2.5HyperbolicManifolds
2.5.1HyperbolicManifoldsofComplexity9
2.6LowerBoundsoftheComplexity
2.6.1LogarithmicEstimates
2.6.2ComplexityofHyperbolic3-Manifolds
2.6.3ManifoldsHavingSpecialSpineswithOne2-Cell
HakenTheoryofNormalSurfaces

3.1BasicNotionsandHaken'sScheme
3.2TheoryofNormalCurves
3.2.1NormalCurvesandNormalEquations
3.2.2FundamentalSolutionsandFundamentalCurves
3.2.3GeometricSummation
3.2.4AnAlternativeApproachtotheTheoryofNormal
Curves
3.3NormalSurfacesin3-Manifolds
3.3.1IncompressibleSurfaces
3.3.2NormalSurfacesin3-ManifoldswithBoundaryPattern
3.3.3NormalizationProcedure
3.3.4FundamentalSurfaces
3.3.5GeometricSummation
3.4NormalSurfacesinHandleDecompositions

4ApplicationsoftheTheoryofNormalSurfaces
4.1ExamplesofAlgorithmsBasedonHaken'sTheory
4.1.1RecognitionofSplittableLinks
4.1.2GettingRidofCleanDiscPatches
4.1.3RecognizingtheUnknotandCalculatingtheGenus
ofaCircleintheBoundaryofa3-Manifold
4.1.4IsM3IrreducibleandBoundaryIrreducible?
4.1.5IsaProperSurfaceIncompressibleandBoundary
Incompressible?
4.1.6IsM3SufficientlyLarge?
4.2Cutting3-ManifoldsalongSurfaces
4.2.1NormalSurfacesandSpines
4.2.2Triangulationsvs.HandleDecompositions

5AlgorithmicRecognitionofSa
5.1Linksina3-Ball
5.1.1CompressingDiscsandOne-leggedCrowns
5.1.2ThinPositionofLinks
……
6ClassiflcationofHaken3-Manifolds
73-ManifoldRecognizer