### 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:

- Hatcher, A., Algebraic Topology, Cambridge University Press, 2002.
- Armstrong, M.A., Basic Topology, Springer (India), 2004.

#### Assignments

Assignments will be posted roughly once in two weeks.

- Connected Components due by Tuesday, Aug 20, 2019.
- 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.

#### Course Details

**Instructor:**Siddhartha Gadgil**E-mail:**siddhartha.gadgil@gmail.com.-
**Office:**N-15, Department of Mathematics. **Timing:**Tuesday, Thursday 8:30 am to 10:00 am.-
**Teaching Assistant:**Pranab Sarkar (pranabsarkar@iisc.ac.in) **Lecture Venue:**LH-5, Department of Mathematics, IISc.