Math 571 Topology



Renzo's class



MWF 3 – 3:50 pm



ENGRG  E 206








Office Hours







Algebraic Topology

Allen Hatcher

Available online here




Bill Fulton’s Algebraic Topology is a beautifully written book. We will probably be picking and choosing things from that book from time to time. E.g. for an analytic presentation of de Rham cohomology etc...



Simplicial Homology

The Prism Operator

Snake Lemma

Degree of Sphere Maps

Universal Coefficients Theorem

Cup Product

de Rham and Compactly Supported Cohomology




PDF file

LaTeX source file



Office hours : there are no official office hours for this class. However, you are very welcome to make an appointment and come ask questions, make comments, or just chat. You can also try showing up at my door anytime. But I might tell you to come back at another time if I am immersed into something else.

Once you get settled, you are warmly invited to tell me what you
do and don't like about me and this class. I  try my best to take criticism very well.

Homework:  OK, this is a graduate course, and so we can be pretty flexible about this. However homework is important stuff to make sure that things sink in and you are not just spending a semester assisting to my creative rambling. Here is some general guidelines I would like to follow:

1.      Grad students who are already working on a thesis problem with an adviser are not required to turn in homework. However they should turn in the midterm.

2.      For other students, if the homework load is incompatible with other grad school priorities (especially for students not specifically working in this area) please talk to me and we can agree on an appropriate fraction  of the workload.

3.      Homework will be collected and checked, but not necessarily graded. Work with the buddy system to make sure you are doing things right, and, in doubt, come ask me.



March 22nd

1)      Prove the 5 L:emma  (Hatcher page 129). Try to prove it yourself before you look at the book…I think it is actually easier.

2)      Hatcher, page 131, Exercises: 1, 4, 12, 17, 18, 22, 29

April 9th

1.      Midterm

2.      Hatcher, page 202, Exercises: 1, 2, 3, 5, 8

May 3rd

      Write up the worksheet on de Rham and CS cohomology






















Exams: I am not extremely fond of exams either, so we will have some alternative ways of evaluating your performance that hopefully can be more productive. These could be in class presentations, compiling good notes etc…I will let you know when I figure out the precise details.