Mathematics 612, Spring 2024

Algebraic Topology II

Mondays, Wednesdays, 1:25-2:40, Physics 259
Office hours: Wednesdays 4:00-5:00, Thursdays 12:00-1:00, and by appointment.


Course information

Course syllabus (updated 1/24) - all of the information below is also contained in the syllabus.

My plan is to post homework assignments and solutions on Canvas.

Textbooks:

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 homework assignments and a take-home final exam for this course.

Course meetings: I will be out of town on February 12 and March 25. There will be make-up classes tentatively scheduled for February 16 and March 29. Please let me know if you have issues with this scheduling.

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: