微分拓扑(续)
2012年2月3日
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Welington de melo的微分拓扑课程己经进行了一半。2月份的课程内容在这里新开一个帖子。
第五周：测地线；Exponential maps;同伦；管状邻域；拓扑度；拓扑度的同伦的不变性；如果值域是
第六周：Morse Theory;The Morse Lemma;gradient field;Quadratic forms,Chain complex;Singular complex;Singular homology;Relative homology;exact sequence;snake lemma;diagram chasing;prism operator,barycentric subdivision,Meyer-Vietoris sequence,five lemma,excision theorem,Morse inequalities;CW-complex;Cellular homology
第七周：differential forms;exterior derivative;the stokes theorem;the de Rham cohomology;poincaré lemma;The cohomology group of 
整个课程的讲义我合在一起放在这里，一共97页。
分类: Differentiable Topology, Maths Barycentric Subdivision, Cellular Homology, CW-complex, De Rham theorem, Diagram Chasing, Differential Forms, Differential topology, Euler Charateristic, Excision Theorem, Exponential Map, Exterior Derivative, Five Lemma, Funndamental Theorem of Algebra, Geodesic, Gradient Field, Hairy Ball Theorem, Homotopy, Hyperbolic Singularity, Intersection Number, Meyer-Vietoris sequence, Morse Inequalities, Morse Theory, Poincaré Duality, Poincaré Lemma, Prism Operator, Quadratic form, Relative Homology, Singular homology, Snake Lemma, the de Rham cohomology, The Morse lemma, The Stokes Theorem, Topological Degree, Tubular Neighborhood, Welington de Melo
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