12/09/21: Now Homework 7 is complete and posted. I apologize for the
delay: I have been swamped by a pile-up of numerous responsibilities,
which are typical for the end of semester: recommendation letter
writing, oral examinations, committee work, etc. I am writing now,
while sitting in a preliminary oral exam in the School of Physics.
12/08/21: Homework 7, due December 15, is partially posted (3
problems). I plan to add a few of problems on Wednesday, December 8.
11/24/21: I will hold pre-Thanksgiving office hours today 2:30-3:20 virtually,
via Zoom. the Zoom link has been sent to you via Google Calendar from
me. Have a great holiday, if I do not see you! Do not hesitate to drop
me an email, should you have questions on or need help with the
homework, even over the Thanksgiving break.
11/20/21: Homework 6 is updated, as promised.
11/19/21: Homework 6, due November 29, is partially posted (6
problems). I plan to add a couple of problems later tonight.
11/10/21: I have just realized that the problem on proving Alexander
duality is too hard in that form and replaced it with a simpler
particular case. Hit the Reload button on the homework to see the
updated version.
11/10/21: As I said in class today, the homework due date is postponed
till Monday, 11/15, because it would help to discuss the cohomology
rings of projective spaces, which we will do no Friday.
11/8/21: I am wondering what you are more interested in continuing
with this term: (1) fiber bundles, (2) fibrations, cofibrations and
homotopy groups, or (3) spectral sequences? Please let me know. Let us
do more fashionable ranked-choice voting: give me your preference #1,
#2, and #3.
11/8/21: If you prefer to continue next semester with this course and
it costs you nothing to register for its continuation, Math 8307, next
term, please do. Then we will see if more people register (I know at
least one student who has not been taking Math 8306 this term but is
interested in Math 8307 next term. If there are more, we can revive
the second semester.
11/5/21: Homework 5, due next Friday, is posted. Should you have any
questions, do not hesitate to ask.
11/5/21: Homework 5, due next Friday, is posted. Should you have any
questions, do not hesitate to ask.
10/22/21: Homework 4, due next Friday, is posted. Should you have any
questions, do not hesitate to ask.
10/14/21: Zane has noticed a typo in Problem 3 on Homework 3: it
should be deg (j-1 γ) = 0 and deg(β
k-1) = 1, rather than the other way around. I apologize and
will correct this shortly.
10/9/21, 1 a.m.: Homework 3 due next Friday is posted. It involves a
little project with 4 problems. Sorry it took me a bit longer thank I
thought to write it.
10/1/21: After today's class, I have immediately realized that showing
that Homℤ(R, I) is injective for an injective or
divisible abelian group I actually involves using the injectivity of I
rather than the more hands-on divisibility property of I. This will be
on the next homework.
9/29/21: Zane has spotted a typo in the cellular chain complex
of RP2 in Problem 2 of Homework 2. Sorry! I have
just corrected it. Please make sure to use today's version.
9/25/21, 12:50 p.m.: Made a few corrections to Homework 2. Make sure
you have the version in which Problem 7 three lines, rather than one.
9/25/21: Homework 2 is posted. Due the coming Friday, before
class. Refresh the Homework web page in your browser, if you do not
see HW 2.
9/24/21: Now all the class meetings in the Google Calendar invites
sent to all of you have Zoom links. It is the same link for all the
class meetings. The Zoom link for the Thursday office hours is
different, but it has also been sent to you via Google Calendar. this
does not mean that I am switching the class to Zoom. I will just be
ready to broadcast the class when some of you have to stay home.
9/22/21: I will be holding my office hours both in person and on Zoom
today, given that some of you are working from home. I have sent a
Zoom link to all of you through Google Calendar. I will try to make it
a rule, but I do not like to carry my laptop to school, so I will need
to make the desktop computer in my Vincent Hall office Zoom
friendly.
9/20/21: I am changing the timing of my Monday office hours slightly
from 1:30-2:20 to 1:25-2:15 to adjust them better to how things are
run at the U. I do not know why I had the 1:30 time in the first
place. Perhaps, just a clerical error on my part.
9/15/21: I have changed Problem 4 on HW 1 from the torus to the real
projective plane, to finish the computation we started today in
class.
9/15/21: I would like to switch my Thursday office hours (2:30-3:20)
to Zoom until further notice. I will send you a link via a Google
Calendar invitation. I would also like to change my Wednesday office
hours to 2:30-3:20 to better accommodate all of you. Let me know if
this (or any of my office hours) conflicts with your schedule.
9/13/21: Since I have posted the first homework on Sunday, I have been
making minor changes to it. When you start working on it, which I urge
you to do now, reload the homework page to make sure you have the
latest version.
9/12/21: Because of a strange euphoria (The first week is over, it is
a weekend now, time to relax!) I had after the first week of
long-awaited in-person classes, I totally forgot to post the first
homework. I do apologize. Now it is posted with a new due date of
Monday, September 20.
9/10/21: I have realized that I have made a terminological error in
class today, when I defined a subcomplex of a CW complex. The notion
of a CW pair was defined correctly: it is a relative CW complex
(X,A) for a CW complex A. But in this case, we do not say A is a
subcomplex of X, neither will X be a CW complex, as a q-cell of X may
be glued on the p-skeleton of A with p > q, which is not supposed to
happen in a CW complex. A subcomplex A of a CW complex X
is the union A of a set of cells of X such that this union A is closed
in X. This condition is stronger than that of a CW pair.
9/8/21: I have redesigned the plan for this semester to accommodate
the switch to a one-semester course. Instead of covering obstruction
theory and Eilenberg-MacLane spaces, we will study spectral sequences
at the end of the term. This is reflected in the updated syllabus.
9/8/21: As I have announced in class, Math 8307 will not be running in
Spring 2022. This semester, I plan to cover many topics from all the
chapters of Hatcher. And you will have options to take Math 8307
later or take 8306-07 entirely, as it will likely be taught
differently by a different instructor. I have updated the syllabus
accordingly.
9/7/21: I have started writing Class Outlines, see the course web
page. I am still working on the homework.
9/7/21: I will check with you at the first class meeting whether my
office hours are okay with you. However, the announced office hours
for this Thursday, January 23, will not work for me. I am moving them
to 1:25-2:15 p.m. just for this week.
9/7/21: I recommend the following way to study for this class. Attend
each class, take notes, participate in class actively. After each
class review your notes and study the corresponding part of the
text. You can find out which part of the text at the Class Outlines
page. Then do the assigned homework problems pertinent to that
material. I also encourage you to work in study groups on the
homework, as most of you did in the first term. Here is a guide
on How
to Form a Successful Study Group.
9/7/21: If you need to register for this course and the system prevents you from doing that, please send a
message to Stephanie Lawson at ugrad@math.umn.edu and ask for a permission number. If
permission is granted, go to OneStop and register.
Last modified: (2021-12-15 11:29:46 CST)