differential geometry - analysis and physics - j. lee

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1、DifferentialGeometry,AnalysisandPhysicsJeffreyM.Lee•c2000JeffreyMarcleeiiContents0.1Preface................................viii1PreliminariesandLocalTheory11.1Calculus................................21.2ChainRule,ProductruleandTaylor’sTheorem.........111.3Localtheoryofmaps.........................112Di

2、fferentiableManifolds152.1RoughIdeasI.............................152.2TopologicalManifolds........................162.3DifferentiableManifoldsandDifferentiableMaps.........172.4Pseudo-GroupsandModelsSpaces.................222.5SmoothMapsandDiffeomorphisms................272.6CoveringsandDiscretegroups.

3、..................302.6.1Coveringspacesandthefundamentalgroup........302.6.2DiscreteGroupActions...................362.7Grassmannianmanifolds.......................392.8PartitionsofUnity..........................402.9Manifoldswithboundary.......................433TheTangentStructure473.1RoughIdeasII

4、............................473.2TangentVectors...........................483.3Interpretations............................533.4TheTangentMap..........................543.5TheTangentandCotangentBundles................553.5.1TangentBundle........................553.5.2TheCotangentBundle...............

5、.....573.6ImportantSpecialSituations.....................594Submanifold,ImmersionandSubmersion.634.1Submanifolds.............................634.2SubmanifoldsofRn..........................654.3RegularandCriticalPointsandValues...............664.4Immersions..............................70iiiivCONTENT

6、S4.5ImmersedSubmanifoldsandInitialSubmanifolds.........714.6Submersions..............................754.7MorseFunctions...........................774.8Problemset..............................795LieGroupsI815.1DefinitionsandExamples......................815.2LieGroupHomomorphisms.....................

7、846FiberBundlesandVectorBundlesI876.1TransitionsMapsandStructure...................946.2Usefulwaystothinkaboutvectorbundles.............946.3SectionsofaVectorBundle.....................976.4Sheaves,Ge