Introduction to Algebraic Topology


Algebraic topology aims to capture essential features of topological spaces in terms of algebraic objects like groups and rings. Topics shall include the Fundamental Group, Seifert van Kampen Theorem, Covering Spaces, and Simplicial Homology. Applications shall include the classification of surfaces, classical theorems like the Brouwer Fixed Point theorem and the Borsuk-Ulam theorem, and a bit of knot theory. We shall mostly refer to the books by Massey and Hatcher.

There will be weekly homework or quizzes based on homework, a midterm and a final exam.

Course description


Week 1 (due 16/8) : Homework 1

Week 2 (due 5/9) : Homework 2

Week 3,4: Assignment will be given by Prof. Datta

Week 5 (quiz on 14/9) : Homework 3

Midterm Solution sketch


Lectures from August 22-31 will be given by Prof. Basudeb Datta.

Midterm exam will be held on Thursday, 21st September from 3:30-5pm.