### 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.

• 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.

#### Midterm Examination

• Date: Thursday, September 26, 2019.
• Time: 8:30 am - 10:30 am.
• Venue: LH-5, Department of Mathematics.

#### Midterm Examination II (Make-up)

This examination is worth $20$ marks. The composite midterm score out of $40$ will be the maximum of the $(\text{midterm 1 score})$ and $(\frac{\text{midterm 1 score}}{2} + \text{midterm 2 score})$.

• Date: Thursday, October 24, 2019.
• Time: 8:30 am - 9:30 am.
• Venue: LH-5, Department of Mathematics.

#### Final Examination

• Date: Wednesday, November 27, 2019.
• Time: 2:00 pm - 5:00 pm.
• Venue: LH-5, Department of Mathematics.