MA 232: Introduction to Algebraic Topology

August, 2019

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.

1. Connected Components due by Tuesday, Aug 20, 2019.
2. Homotopy and Fundamental Groups due by Tuesday, Sep 17, 2019.
3. Graphs and Free Products due by Thursday, Nov 7, 2019.

Final Exam Graded papers

The final examination has been graded. Please check your answer papers, totalling and grade entries at one of the following times:

• Dates: Monday, December 2, 2019 and Tuesday, December 3, 2020.
• Time: From 8:30 am to 12:15 pm.

As I will enter the grades in the system on Wednesday, December 3, 2019, please ensure that you check everything during these times.