
Renzo's class 


MWF 10 – 10:50 am 


ENGRG E 206 






TEXTBOOK:
Algebraic Topology
Allen Hatcher
Available online here
OTHER GOOD BOOKS:
For the part of general
topology I will not be following any book in particular. I believe any
reasonable book could be a good reference if you would like one. For example Armstrong’s book is well written and pretty
essential. Munkries is a bit more hard core and dry, contains
more information (probably more than you care about). Schick is quite elementary and a bit funky, but will be
the book for you if you are fascinated by exotic topologies...
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.
PROJECTS AND SUCH
Project 1: Making New Spaces from Old Ones (LaTeX source)
Project 1 with solutions (Part 1) (Part 2)
Compactifications (LaTeX
source)
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.
The tables of the law for this class are contained in the
following document:
Syllabus
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.
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: 

Friday Aug 28^{th} 
Life with a metric (LaTeX source) This worksheet is intended to present the intuitive version of topology when a space is endowed with a notion of distance. Although in this class we will not always have such a luxury, it is a good thing to anchor your intuition to. Friday’s class, if you wish,
can be devoted to discussion about this homework and the relation between the
abstract definitions of the first
couple days of class and those in this worksheet. But this will happen ONLY if you ask
questions, otherwise I’ll assume all is good and move on. 
Friday Sep 11^{th} 
Some
more basic concepts (LaTeX source) We continue exploring
with the basic concepts in topology. We define some more unusual topology (like the half line
and the Zariski topology) and explore on them the concepts illustrated in
class. We also introduce some new notions (dense sets, separation axioms). If
you are unfamiliar with these concepts pay special attention to those
exercises! 
Friday Sep 18^{th} 
Writeups for projects
due. Please LaTeX your answer in such a way that I can compile them in a
unique document! 
Friday Sep 25^{th} 

Friday Oct 9^{th} 
Write up a (art most) three page account of the classification theorem for compact surfaces. Give good outlines, choose carefully what details to give. Make it pleasant to read! 
Friday, Oct 23^{rd} 
Exercises 5, 8, 12, 18, 20 pages 3839 of Hatcher (current webpage version) Exercise 9 page 53 
Friday Nov 20^{th} 
Exercises 3, 4 (hint, pull the diameter outside the sphere!), 14, 18, 27 on pages 79 and following of Hatcher. 












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.