MAT 531 (Spring 1996) Topology/Geometry II


The Official MAT 531 Syllabus

Differentiable manifolds and maps
Inverse and implicit function theorems
Submanifolds, immersions and submersions
Vector fields and flows
Tangent bundle
Differential forms:
-exterior derivative
-Stokes' Theorem
-integration and volume on manifolds
-brief description of de Rham cohomology
Lie derivative and bracket
Frobenius theorem
Introduction to Lie groups and to the classical groups