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

Core topics in homology and cohomology theory including CW complexes, universal coefficients, and Poincare duality. Higher homotopy groups.

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. Higher homotopy groups, Whitehead and Hurewicz theorems
  7. Selection from advanced topics such as: classification of vector bundles, K-theory, Cech cohomology, cobordism theory, spectral sequences, stable homotopy theory/generalized cohomology theories