Introduction to Algebraic Topology

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

Homework

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

Supplementary material

Surfaces are triangulable by Doyle and Moran

Classification of surfaces by Zeeman

Hawaiian earring group by Cannon and Conner (see Theorem 2.6)

Announcements

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.