### 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.