Introduction to Algebraic Topology

Department: 
MATH
Course Number: 
4432
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Every odd spring semester

Introduction to algebraic methods in topology. Includes homotopy, the fundamental group, covering spaces, simplicial complexes. Applications to fixed point theory and group theory.

Prerequisites: 

MATH 4317

Course Text: 

At the level of Algebraic Topology: An Introduction, by William S. Massey

Topic Outline: 
  • Manifolds
  • Triangulations of compact surfaces
  • Euler characteristic of a surface
  • Classification theorem for compact surfaces
  • Fundamental group
  • Homotopy type and homotopy equivalence of spaces
  • Free groups and free products of groups
  • Presentation of groups by generators and relations
  • Seifert and Van Kampen Theorem
  • Fundamental group of a compact surface
  • Knot groups
  • Other topics of interest