05/18/05: The mean on the third homework is 40 out of 60, with
a median of 38.5. The top score is 52. You may get your homework from
your mailbox. Thank you all for the wonderful semester! It was a
pleasure to learn things with you:-)
05/18/05: The mean on the third homework is 40 out of 60, with
a median of 38.5. The top score is 52. You may get your homework from
your mailbox. Thank you all for the wonderful semester! It was a
pleasure to learn things with you:-)
05/05/05: The mean on the second homework is 46.4 out of 50,
with a median of 48. The top score is 50. You may get your homework
from your mailbox.
04/24/05: The last problem set, due Monday, May 9, is posted!
04/05/05: As Dan noticed, the cohomology in the problem (Problem Set
5) on Moore spaces must be changed to homology. I have changed that in
the new version of the problem set.
03/31/05: A new problem set, Problem Set 5, is posted and due Friday,
April 15!
03/27/05: I am sorry about this short a notice, but I have to cancel
our Monday, March 28, class, because of a family emergency. I will
see you on Wednesday.
03/09/05: The mean on the first Spring homework is 47 1/3 out
of 60, with a median of 49. The top score is 53. I planned to put the
homeworks in your mailboxes at any cost this night, but feel to tired
this late and hope you will excuse me, if I do it tomorrow
morning:-(
02/25/05: I have to change my office hours Thursday permanently to
1:25-2:15 pm, because of the Topology Seminar meeting at 11:15 on
Thursdays.
2/21/05: The Homework 1 due date is postponed further till Friday,
February 25, because we still need to learn fiber sequences!
2/16/05: The Homework 1 due date is postponed till Wednesday, February
23!
2/9/05: Josef has noticed a notational error in a proposition we had
in class, needed for Problem 4 of the homework. Here is a
correction. Proposition: A map i: A --> X is a cofibration, iff the
map j: Mi --> XxI defined by j(a,t) = (i(a),t) and j(x,0) = x has a
left inverse (i.e., r such that rj = id). What we had in class was the
following obvious Corollary: An inclusion i is a cofibration, iff Mi
is a retract of XxI. But this is not needed to do Problem 4.
Also, in Problem 3, we are talking about points in U.
2/7/05: In Problem 8 to Section 4.3 of Hatcher, the equation ps = id
must be replaced with \pi s = id. (Thanks to Josef).
2/6/05: I have to be at a meeting Friday, February 11, at 1:25
p.m. and therefore am moving my office hours that day to
11-noon.
2/2/05: A new problem set, Problem Set 4, is posted and due Friday,
February 18!
1/18/05: Welcome to the new semester! I hope it will be full of math
discoveries and adventures for you. I have changed slightly the old
syllabus posted on the class web page. The changes concern the new
room, VinH 311, and coverage for the second semester: I moved the
topics of homotopy groups and fibrations and cofibrations, which we
have not covered in the first semester, over to the second
semester. We will be studying homotopy theory, which is the
culminating point of modern Algebraic Topology. I am looking forward
to seeing you tomorrow in class!
12/13/04: I have just realized that I will have to attend a seminar
tomorrow (Tuesday, December 14) from 10 to 11 am, just when I
scheduled my extra office hours previously. I am moving my Tuesday
office hours then to 11:00 to noon. I am sorry.
12/13/04: The last problem set due date is postponed till 5 pm
Friday, December 17.
12/13/04: Extended office hours for the finals week, December
13-17: Mon 11-noon, Tue 11-noon, Wed 11-noon, Fri 1:30-3:30 p.m.,
and by appointment. Note that I will be out of town Thursday and have
to cancel my regular office hours on Thursday.
12/13/04: Hinted by Antoine again, I have moved the hint back from (3)
to (2) in Problem 3 and explained why dealing with that funny
composition of the three maps in (2) was interesting. Sorry about the
confusion. Send me a message, if you have questions.
12/10/04: Hinted by Antoine, I have corrected Problems 1 and 3 on the
homework. In Problem 1, I added a finite-dimensionality assumption,
while in Problem 3, I moved the hint from (2) to (3). Sorry about
trying to send you on the wrong track:-) Send me a message, if you
have questions. I am going to announce more office hours for the
beginning of the next week.
12/05/04: The mean on the second homework is 35.2 out of
60. The maximal score is 52.
12/03/04: I have corrected a minor misprint in Problem 1 on Homework 3
(changed X to Y in one place on the left-hand side of the formula) and
somewhat reworded the problem to make it clearer. If have problems
downloading a new version, it may help to clear Cache under
Preferences -> Advanced.
11/16/04: A hint to Problem 2 on p. 155 of Hatcher's text: use lifting
properties of covering spaces (see Hatcher, Section 1.3) to lift a map
from S^{2n} to RP^{2n} to a map from S^{2n} to itself.
11/10/04: The problem on Homework 2 dealing with computing the mod 2
homology of the projective space is replaced with the same but for the
homology of the Klein bottle.
11/03/04: Le homework nouveau est ajourné au 17 novembre.
11/01/04: Le homework nouveau est
arrivé!
10/18/04: The mean on the first homework is 43.6 out of 70.
10/05/04: The textbook "Topology and Geometry" by Glen Bredon is now
on two-hour reserve in the library.
10/04/04: Because of Penrose's colloquium on Tuesday, I would like to
change my office hours this week back to the regular schedule: Wed
11-noon, Thu 11-noon, Fri 1:30-2:30 p.m. I recommend each of you
to attend the colloquium, because it was Penrose, who at some point
changed the world of theoretical physics using topological methods.
10/04/04: In addition to textbooks by Hatcher, Selick, and Sato, I am
requesting the text "Topology and Geometry" by Glen Bredon to be put
on two-hour reserve in the library. I do apologize, if it happens to
be recalled from one of you.
09/27/04: Changes in office hours for the two coming weeks, Sep 27
- Oct 8. This (Sep 27) week's office hours (to cover for the
canceled ones on Thursday): Tuesday 12:20 - 1:20, Wednesday 11 - noon,
Friday 1:30-2:30. Next (Oct 4) week's office hours (10/04/04: changed
back to regular schedule, because of Penrose's lecture): Wednesday 11
- noon, Thu 11-noon, Friday 1:30-2:30.
09/24/04: I have moved my office hours from Tuesday to Thursday
11-noon. Unfortunately, next Thursday, September 30, I will be out of
town and not hold these office hours.
09/20/04: The first problem set is posted and due Monday, October
4.
09/16/04: I will be posting homeworks two weeks before they are
due. The first one will be due sometime in the beginning of
October.
09/16/04: In addition to Hatcher's textbook, there is another text on
reserve in the library for our class: Introduction to Homotopy Theory
by P. Selick. I have also requested Algebraic Topology: an Intuitive
Approach by H. Sato to be put on reserve, but the text is checked out
and is being recalled.
09/15/04: I will have to drive to Chicago Friday, September 15, and
cancel my Friday office hours, which are normally from 1:30 through
2:25 pm. If you would like to talk to me, please, do that sometime
after 2 pm Thursday or right after class Friday.