
Renzo's class 


MWF 3 – 3:50 pm 


ENGRG E 206 






TEXTBOOK:
Algebraic Topology
Allen Hatcher
Available online here
OTHER GOOD BOOKS:
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...
PROJECTS AND SUCH
Universal Coefficients Theorem
de Rham and Compactly Supported Cohomology
LaTeX CHEATSHEET:
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
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.
DATE DUE: 

March 22^{nd} 
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 9^{th} 
1. Midterm 2. Hatcher, page 202, Exercises: 1, 2, 3, 5, 8 
May 3^{rd} 
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.