Math 540: Introduction to Algebraic Topology I

Fall 2021

Instructor: Kristen Hendricks

Email: kristen. hendricks at

Office Hours: T 3-4, Th 11-12 over zoom; Meeting ID 570 840 4797, passcode cycle

A printable copy of the syllabus is here.

Location and Time: TTh 1:00-2:20 in Hill 005.

Prerequisites: Point-set topology and abstract algebra (groups, rings, fields).

Topics: This is a standard first course in algebraic topology. We will cover the fundamental group, covering spaces, and singular, simplicial, and cellular homology and cohomology. Along the way we will prove some rather nice applications.

Notes: Lecture notes and audio recordings will be posted here shortly after class. (Usually the lecture notes will in fact be available some time before class.)

Homework: Homework exercises for each week will be posted some time before the start of Tuesday’s lecture, and the file will be shared in class. Registered students are expected to write up and hand in roughly half the homework exercises. Submission will be accepted either in hard copy or (mildly preferred) canvas upload.

Text: The textbook for this course is A. Hatcher’s Algebraic Topology, which is available for free on his website. It is a very friendly textbook; doing the reading before coming to lecture is advised. We will be covering roughly Chapters 0-3, excluding the special topics. Other good books on the same material include:

Covid Safety: Everyone is expected to wear a mask covering the nose and mouth to class.


Week 1 Exercises.

Week 2 Exercises.

Week 3 Exercises.

Week 4 Exercises.