### MA 232: Introduction to algebraic topology

#### Prerequisite courses: MA 231 and MA 212

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. Armstrong, M.A., Basic Topology, Springer (India), 2004.
2. Hatcher, A., Algebraic Topology, Cambridge University Press, 2002.
3. Kosniowski, C.A., First Course in Algebraic Topology, Cambridge Univ. Press, 1980.
4. Croom, F.H., Basic Concepts of Algebraic Topology, Springer-Verlag, 1978.

#### All Courses

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265
E-mail: chairman.math[at]iisc[dot]ac[dot]in