Algebraic Topology I

Department: 
MATH
Course Number: 
6441
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Every Spring Semester

The fundamental group, covering spaces, core topics in homology and cohomology theory including CW complexes, universal coefficients, and Poincare duality.

Prerequisites: 

MATH 4107, MATH 4317 or MATH 4431, or consent of instructor

Course Text: 

At the level of Hatcher, Algebraic Topology

Topic Outline: 
  1. Singular homology and chain complexes
  2. Homological algebra, universal coefficients
  3. CW complexes
  4. Singular cohomology
  5. Products and Duality on manifolds
  6. The fundamental group and Van Kampen’s theorem.
  7. Covering space and connections with the fundamental group.