### 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.)

Back to Top/Geom II base-page

*Tony Phillips*

Math Dept SUNY Stony Brook

April 30 1996