topological and geometric properties of low dimensional manifolds

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1、TopologicalandGeometricPropertiesofLowDimensionalManifoldsKyosukeOta(HirosakiUniversity)CONTENTS1.SimplicialComplexes11.1SimplicialComplexes:::::::::::::::::::::::::::::::::11.2OrientationsofSimplicialComplexes::::::::::::::::::::::::21.3StarNeigborhoodsandLinkNeigborhoods::::::

2、:::::::::::::::31.4SubdivisionsofSimplicialComplexes::::::::::::::::::::::::31.5Simplicialmaps::::::::::::::::::::::::::::::::::::52.CombinatorialManifolds72.1Triangulations:::::::::::::::::::::::::::::::::::::72.2CombinatorialManifolds:::::::::::::::::::::::::::::::72.3RegularN

3、eigborhoods:::::::::::::::::::::::::::::::::92.4IntersectionsofSubmanifolds:::::::::::::::::::::::::::::113.HomologyGroupsandHomotopyGroups153.1HomotopyGroup:::::::::::::::::::::::::::::::::::153.2HomologyGroup::::::::::::::::::::::::::::::::::::163.3Cohomologygroup:::::::::::::

4、::::::::::::::::::::::163.4EulerCharacteristic::::::::::::::::::::::::::::::::::173.5RepresentationsofGroups::::::::::::::::::::::::::::::184.ExamplesofCombinatorialManifolds214.11;2;3-CombinatorialManifolds::::::::::::::::::::::::::::214.2OrientableSurfacesandNon-orientableSurf

5、aces::::::::::::::::::234.3OrientationsofSimpleClosedCurves::::::::::::::::::::::::244.4CombinatorialSpheresandCombinatorialBalls::::::::::::::::::245.Handlebodies295.1DenitionofHandlebody:::::::::::::::::::::::::::::::295.2PlanarSurfaces:::::::::::::::::::::::::::::::::::::295

6、.3CompleteMeridianDiskSystem:::::::::::::::::::::::::::306.HeegaardSplittingsandHeegaardDiagrams336.1HeegaardSplittings::::::::::::::::::::::::::::::::::336.2HeegaardDiagrams::::::::::::::::::::::::::::::::::34III7.GenusesandFundamentalGroups377.1FundamentalGroups:::::::::::::::

7、::::::::::::::::::377.2GenusesoftheCombinatorialmanifolds:::::::::::::::::::::::388.LensSpaces398.1SimpleClosedCurvesintheToruses:::::::::::::::::::::::::398.2LensSpaces:::::::::::::::::::::::::::::::::::::::408.3ClassicationofLensspaces:::::::::::::::::::::::::::::429.Connecte

8、dSums439.1ConnectedSums::::::::::::::::::::::::