© | Dror Bar-Natan: Classes: 2004-05: Math 1300Y - Topology: | (2) |
Next: Class Notes for Thursday September 9, 2004
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**URL:** http://www.math.toronto.edu/~drorbn/classes/0405/Topology/.

**Agenda:** Learn about the surprising relation between the easily
deformed (topology) and the most rigid (algebra).

**Instructor:** Dror Bar-Natan, drorbn@math.toronto.edu,
Sidney Smith 5016G, 416-946-5438. Office hours: Thursdays 12:30-1:30.

**Teaching Assistant:** Toan Ho Minh, hmtoan@math.toronto.edu,
Sidney Smith 623A, 416-978-2967.

**Classes:** Tuesdays 1-3 and Thursdays 2-3 at Sidney Smith 5017A.

**Optimistic Plan:**

- Point set topology: Topological spaces and continuous functions, connectedness and compactness, countability and separation axioms.
- Homotopy: Fundamental group, Van Kampen theorem, Brouwer's theorem for the 2-disk. Homotopy of spaces and maps, higher homotopy groups.
- The language of category theory.
- Covering theory, universal coverings.
- Homology: Simplicial and singular homology, homotopy invariance, exact sequences, Mayer-Vietoris, excision, Brouwer's theorem for the n-disk, degrees of maps, CW-complexes, Euler characteristic, a word about the classification of surfaces.
- Cohomology: Cohomology groups, cup products, cohomology with coefficients.
- Topological manifolds: Orientation, fundamental class, Poincare duality.

**Textbooks:** We will mainly use James Munkres' Topology
(ISBN 0-13-181629-2) and Allen Hatcher's Algebraic
Topology (Free! ISBN 0-521-79540-0). Additional texts by Bredon,
Bott-Tu, Dugundji, Fulton, Massey and others are also excellent.

**Lecture Notes:** I'll be happy to scan the lecture notes of one
of the students after every class and post them on the web. We need a
volunteer with a good handwriting!

**The Final Grade:** For students taking this course all year the
final grade will be determined by applying an increasing continuous
function (to be determined later) to
*0.2HW+0.15TE1+0.15TE2+0.5F*, where *HW*, *TE1*,
*TE2* and *F* are the HomeWork, Term Exam 1, Term Exam 2
and Final grades respectively. For students taking only the second half
of the course the final grade will be determined by applying an
increasing continuous function (possibly a different one) to
*0.2HW+0.2TE2+0.6F*.

**Homework:** There will be about 12 problem sets. I encourage
you to discuss the homeworks with other students or even browse the
web, so long as you do at least some of the thinking on your own and
you write up your own solutions. The assignments will be assigned on
Thursdays and each will be due on the date of the following assignment,
in class at 3PM. There will be 10 points penalty for late assignments
(20 points if late by more than a week and another 10 points for every
week beyond that). Your 10 best assignments will count towards your
homework grade. If you are only taking the second half of the course,
you'll only see 7 of the assignments and only your best 6 will count
towards your homework grade.

**The Term Exams:** Term exam 1 and Term Exam 2 will take place
in the afternoons or evenings outside of class time, on the weeks of
November 15 and February 28, respectively. They will be 2 hours long.

**Feedback:** I'd be very happy to hear from you. There's a link
to a feedback form at the top of this class' web site (and here). Anonymous messages are fine, provided
they are written with good intent. Though remember that if I don't know
who you are I may not be able to address your concern. You will each be
*required* to use this feedback form at least once, on the
third week of classes (see below).

**Class Photo:** To help me learn your names, I will take a class
photo on Thursday of the third week of classes. I will post the picture
on the class' web site and you will be *required* to use the feedback form to identify yourself in the
picture.