Mathematics 612, Spring 2022

Algebraic Topology II

Mondays, Wednesdays, 10:15-11:30 am, Physics 205
Office hours: Mondays 2:00-3:00, Tuesdays 3:00-4:00, and by appointment.

First 3 classes: As per university policy, our first 3 class meetings (1/5, 1/10, 1/12) will be on Zoom. Hopefully we'll have in-person classes after that. The Zoom link for our online classes is available on the Sakai page for our course. Alternatively, you can manually enter the following information in Zoom:
Meeting ID 920 9519 7016
Password = 10-letter word that appears in the titles of the first 3 parts of the course, according to my lecture notes below. (The Zoom address will be the same for all online classes.)

Course information

Course syllabus - all of the information below is also contained in the syllabus.

Homework assignments and solutions will be posted on Sakai.


We will use Hatcher for the first portion of the course (the first few weeks), when we discuss singular cohomology. The rest of the course will be based on Bott and Tu, which is the "official" text for the course.

Prerequisite: Math 611 or familiarity with equivalent material (fundamental group, simplicial/singular homology, CW complexes; essentially the first two chapters of Hatcher). Math 620 or familiarity with basic differential topology (smooth manifolds, tangent/cotangent bundle, differential forms) will also be assumed, but this isn't an ironclad prerequisite; please talk to me if you don't have previous background in smooth manifolds.

Grading: There will be weekly/biweekly homework assignments and a take-home final exam for this course.

Here are the topics that I plan to cover in the course:

Course lecture notes

For your convenience, my lecture notes from a previous time I taught this course (Fall 2014) are available. I will probably be following these notes fairly closely though not exclusively. Here they are: