MATH 4530: Introduction to Topology

A simplicial complex.

Topology is the study of topological spaces: point sets endowed with "nearness" information. The purpose of this course is to develop our intuition about topological spaces as we study key examples, learn various constructions and prove fundamental theorems of topology.

This course, held Fall 2022 at Cornell University, will be divided into two parts: the first part will cover the basics of general point-set topology and the second part will introduce cellular complexes and algebraic topology.

Basic Information

Evaluation

Schedule

The plan for the first part of the course is to cover most of the material from Chapter 2 to Chapter 5 of the textbook. In the second part, we will cover most of Chapter 9 and Chapter 11 and then cover some selection of topics from chapters 12, 13 and 14.

The textbook sections indicated in the schedule below will be modified and updated as we go along.

Week Lectures Textbook sections
Tue. Thur.
1 Aug. 23Aug. 25 §12 – §14
2 Aug. 30Sep. 1 §15 – §16
3 Sep. 6Sep. 8 §17 – §18
4 Sep. 13Sep. 15 §19 – §20
5 Sep. 20*Sep. 22 §21 – §22
6 Sep. 27Sep. 29 §23 – §25
7 Oct. 4Oct. 6 §26 – §28
8 Fall break Oct. 13 §29 – §30
9 Oct. 18Oct. 20 §31 – §33
10 Oct. 25Oct. 27 §34 – §37
11 Nov. 1*Nov. 3
12 Nov. 8Nov. 10
13 Nov. 15Nov. 17
14 Nov. 22Thanksgiving
15 Nov. 29Dec. 1

* In-class preliminary exam on this date.

Homework

Homework assignments will be posted to the MATH 4530 gradescope.