Instructor: Mladen Bestvina
Office: JWB 210
Office hours: By appointment
Meets: MWF 10:45-11:35
in JWB 333
Midterm: Friday, Oct. 4
Final: Monday, December 9, 2024, 10:30 – 12:30
Text: There are many textbooks on
differentiable manifolds. We'll mainly be using
but here are some others that you may find useful:
The main drawback of Guillemin-Pollack is that
manifolds are defined as subsets of Euclidean space instead of
the more modern and standard definition via charts. To bridge
this difference I wrote some notes. The last few weeks of classes
we'll switch to another book (probably Spivak) to cover Lie
brackets, Lie derivatives, foliations etc.
Homework:
It will be assigned weekly. You
are encouraged to work in groups, but what you write should be
your own work and you should list the other people in your
group. It will be due every week on Mondays at 9 am and you
should turn it in through canvas in latex. Late
homework is not accepted but the lowest two scores are dropped
from the count. You should read the assigned reading for the
week before the corresponding lecture. I will also
typically give out several problems each week that you are not
required to turn in.
Problem sessions: We'll
have a problem session every other week where you are
expected to present solutions to unassigned problems. It'll
be on Fridays 3-4 in LCB 222. The first session: 8/30. The
signup sheet is here.
Grading:
The final grade is based on homework (30%), problem session
activity (10%), the midterm (20%) and the final (40%).
| Week |
Reading |
Homework |
Due Date |
| 1 |
Notes Ch 1, G-P 1.1 |
1,4,6,9,12 from hw01, if it's helpful here
is the tex file. |
8/26 |
| 2 |
Notes Ch 2-3, G-P 1.2-1.4 (I
periodically update the notes, you may want to download
again) |
1,4,11,12,13 from hw02
and the latex
file. |
9/3 |
| 3 |
It's a short week. We'll do some odds and
ends and start with partitions of unity |
1,3,9 from hw03 and
the latex file |
9/9 |
| 4 |
partitions of unity and transversality,
Sard's theorem |
1,3,7,8,9 from hw04
and the latex
file |
9/16 |
| 5 |
Tangent bundles, Whitney embedding, Morse
functions |
1,2,3,5,7 from hw05 and
the latex
file |
9/23 |
| 6 |
Manifolds with boundary, normal bundles,
tubular neighborhood theorem |
4,5,6,7,10 from hw06
and the latex
file |
9/30 |
| 7 |
Intersection theory mod 2. |
No homework. Get ready
for the exam on Friday. |
|
| 8 |
Oriented intersection theory, Poincare-Hopf |
1,3,6,8,11 from hw07 and
the latex file |
10/21 |
You can contact me by email.