MAT 531 (Spring 1996) Topology/Geometry II

Week by Week

Week 1: Quotient Topology.
Week 2: Implicit Function Theorem.
Week 3: Inverse Function Theorem, Smooth manifold, tangent vector, tangent bundle, coordinate bundle.
Week 4: Reconstruction of bundle from transition functions, the differential of a smooth map, local topology of immersions and submersions, submanifold.
Week 5: Transversal intersection, approximation of map by map having 0 as regular value.
Week 6: Cotangent bundle, vectorfields and 1-forms, differential forms.
Week 7: Integration of forms.
Week 8: Manifold with boundary, Stokes' Theorem, Definition of de Rham cohomology, cochain complex.
Week 9.1: Homotopy Theorem.
Week 9.2: Mayer-Vietoris Theorem.
Week 10: Integral curves of a vectorfield.
Week 11: 1-parameter groups of diffeomorphisms.
Week 12: Lie derivative. Definition of singular simplex, singular chain.
Week 13: Singular homology, Mayer-Vietoris Theorem
Week 14: Mayer-Vietoris Theorem (cont.)

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Tony Phillips
Math Dept SUNY Stony Brook
April 30 1996