## Differential Topology

Department:
MATH
Course Number:
6452
Hours - Lecture:
3
Hours - Lab:
0
Hours - Recitation:
0
Hours - Total Credit:
3
Typical Scheduling:
Every Fall Semester

The differential topology of smooth manifolds.

Prerequisites:
Course Text:

At the level of A Comprehensive Introduction to Differential Geometry, Vol. 1, Spivak or Differential Topology Guillemin and Pollack

Topic Outline:
• Definition of differential manifolds
• Vectors bundles
• Tangent vectors, vectors fields and flows
• Smooth functions on manifolds, derivatives
• Regular values, Morse functions, transversality, degree theory
• Tensors and forms
• Integration on manifolds, Stokes theorem and de Rham cohomology