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: 

MATH 4431

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