MA 232: Introduction to Algebraic Topology

October 2020

Syllabus

The fundamental group: Homotopy of maps, multiplication of paths, the fundamental group, induced homomorphisms, the fundamental group of the circle, covering spaces, lifting theorems, the universal covering space, Seifert-van Kampen theorem, applications.

Simplicial Homology: Simplicial complexes, chain complexes, definitions of the simplicial homology groups, properties of homology groups, applications.

Suggested books:

  1. Hatcher, A., Algebraic Topology, Cambridge University Press, 2002.
  2. Armstrong, M.A., Basic Topology, Springer (India), 2004.

Assignments

Assignments will be posted roughly once in two weeks.

Course Details

This course will be offered online, and details will be posted as they become available.