Math 672: Topology II

Office hours moved 3 May

I will not be available Tuesday 3 May for office hours. Instead I will move this office hour to Thursday 5 May from 5–6pm. You should be able to use the same Zoom link for Tuesday on Thursday. Wednesday’s office hour will run as usual.

Final Exam Information

Our final exam will be a take-home exam. The exam will be cumulative. It will be distributed by email by noon on the first day of finals week (6 May) and must be submitted by 5pm on the last day of finals week (12 May). Submissions will be done online through moodle; more information about this will come soon. In the meantime, please be aware of the following:

The Moodle course can be found here. At the moment there is nothing useful there.


Prof. Paul Gunnells, LGRT 1115L, 545–6009, gunnells at math dot umass dot edu.

The best way to contact me is by email at my math department address, given above using a sophisticated encryption scheme. Please be sure to include “Math 672” in your subject, otherwise it might get lost in the torrents of bureacratic email I receive.

Please do not leave a message on my office phone, or send an email/message through any other platform or to any other email address (the university has some others on various pages that it thinks are mine, I don’t know why … in particular do not use anything with in it). I generally respond to email within two business days, although I typically don’t deal with email in the evenings or on weekends.

Office Hours

Tuesdays, 5–6pm. Wednesdays, 7–8pm. Office hours Wed 23 March will be canceled.


This course, together with Math 671, presents topics in point-set topology and algebraic topology. In the first semester, the emphasis was on point-set topology and the beginnings of algebraic topology (specifically the fundamental group). The second semester treats homology and cohomology.


In addition, you might find the following helpful:

Over the course of 671–672, we plan to cover chapters 1–4 from Lee and chapters 0–3 from Hatcher.

Any of the following can be used to compute the Smith normal form (or the elementary divisors) of an integral matrix (you will have to search the docs to figure out how to do it).


The grading will be based on problem sets, a final exam, and class participation.


The best way to get help is to ask questions during lecture and during office hours. Forming study groups to work on problems together is also a great idea and is strongly encouraged. However you must submit your own writeups to problems and indicate if you collaborated with anyone else. You also must self-monitor to make sure that you are learning the material yourself.

Please note that it is not possible for me to answer mathematical questions by email. In my experience this just causes more confusion than it helps. It’s much better to ask me in person or office hours (which I want you to do!).

Homework assignments

Homework is assigned here approximately weekly. Assignments may overlap.