Topology and Manifolds

4 Credits.

Smooth manifolds (with and without boundary) and smooth maps; Regular value theorem; Tangent spaces and vector fields; Flows of vector fields; Lie derivatives and general vector bundles; Orientability; Degree of maps; Euler characteristic and Poincare-Hopf Theorem; Covering Spaces and fundamental groups for manifolds; Exterior algebra and differential forms; Integration on manifolds; Stokes Theorem.