### 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.

#### 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.