Computational Topology

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1、COMPUTATIONALTOPOLOGYANINTRODUCTIONHerbertEdelsbrunnerandJohnHarerDepartmentsofComputerScienceandMathematicsDukeUniversityToourfamiliesandfriendsTableofContentsPartAIGraphs11ConnectedComponents22CurvesinthePlane93KnotsandLinks154PlanarGraphs22Exercises29IISurfaces311Two-dimensionalMani

2、folds322SearchingaTriangulation393Self-intersections454SurfaceSimplification51Exercises57IIIComplexes591SimplicialComplexes602ConvexSetSystems673DelaunayComplexes744AlphaComplexes81Exercises88PartBIVHomology911HomologyGroups922MatrixReduction983RelativeHomology1044ExactSequences111Exerc

3、ises118VDuality1211Cohomology1222Poincar´eDuality1283IntersectionTheory1324AlexanderDuality136Exercises139VIMorseFunctions1411GenericSmoothFunctions1422Transversality1483PiecewiseLinearFunctions1544ReebGraphs160Exercises167PartCVIIPersistence1691PersistentHomology1702EfficientImplementat

4、ions1783ExtendedPersistence1844SpectralSequences191Exercises198VIIIStability2011TimeSeries2022StabilityTheorems2083LengthofaCurve2154BipartiteGraphMatching221Exercises228IXApplications2311ImageSegmentation2Elevation3GeneExpression4LocalHomologyforPlantRootArchitectureExercisesPartDXOpe

5、nProblems2371ComplexityofReidemeisterMoves2382Shellinga3-ball2393GeometricRealizationof2-manifolds2414EmbeddinginThreeDimensions2425EquipartioninFourDimensions2436Running-timeofMatrixReduction2447Multi-parameterPersistence2458UnfoldingPLCriticalPoints2469PLintheLimit24710CountingHalvin

6、gSets248Index259PrefaceThelasttenyearshavewitnessedthatgeometry,topology,andalgorithmsformapotentmixofdisciplineswithmanyapplicationsinsideandoutsideacademia.Weaimatbringingthesedevelopmentstoalargeraudience.Thisbookhasbeenwrittentobetaught,anditisbasedonnotesdevelopedduringcoursesdeli

7、veredatDukeUniversityandattheBerlinMathematicalSchool,primarilytostudentsofcomputerscienceandmathematics.Theorganizationintochapters,sections,exercises,andopenproblemsreflectstheteachingstylewepractice.Eachchapterdevelopsamajortopicandisworthabouttwoweeksofteaching.Thechaptersaredivid