# Math 5193 - Smooth Manifolds

Lectures: M 2:30 - 3:45, Th 2:30-3:45, MSCS 509
Problem session: F 2:30-3:20, MSCS 509

## Lecturer:

Jiří Lebl
Web: http://math.okstate.edu/people/lebl/
Office: MSCS 505
Office hours: Monday 4-5pm, Wednesday 11:30-12:30pm, Thursday 4-5pm, and by appointment at other times.
Office phone: (405) 744-7750
Email: lebl at okstate dot edu

## Text/Schedule:

John M. Lee, Introduction to Smooth Manifolds, Second edition, 2013, Springer.

The link above is a link to Springer, and we have electronic access to the book at OSU, so you can read it online if you wish (as PDFs).

We will have weekly homework and we will have a problem session to go over the homework problems in (you should try to solve them before hand). Your grade will be based on participation in the problem session.

## Homework:

Homework 1, for problem session on Friday Aug. 21:
page 30: 1-3, 1-4, 1-5

Homework 2, for problem session on Friday Aug. 28:
page 30: 1-6, 1-7, 1-8, 1-9, 1-10 (feel free to "pick and choose" of course, these should all be fairly straight forward though).

Homework 3, for problem session on Friday Sep. 4:
page 30: 1-11, 1-12
page 48: 2-1, 2-3, 2-5, 2-6, 2-7, 2-9, 2-10 (you should definitely try this one)

Homework 4, for problem session on Friday Sep. 11:
We can go through more of hw 3. And also
page 75: 3-1, 3-5

Homework 5, for problem session on Friday Sep. 18:
We can go through more of hw 3. And also
page 75: 3-2, 3-3, 3-4, 3-6, 3-8

Homework 6, there is no problem session on Friday, though you guys can still meet if you want to, I can't be there:
page 95: 4-1, 4-5, 4-6, 4-8, 4-13

Homework 7, for the problem session on Friday Oct. 2:
page 123: 5-1, 5-4, 5-5, 5-6, 5-7, 5-11, 5-15

Homework 8, unfortunately no class on Friday, but look at these problems:
page 123: 5-16, 5-18, 5-19, 5-21, 5-22

Homework 9, for the problem session on Friday Oct. 16:
We can also look at the previous problems.
page 147: 6-1, 6-2

Homework 10, for the problem session on Friday Oct. 23:
page 147: 6-5, 6-8, 6-9, 6-11, 6-14, (and maybe 6-16, 6-17)

Homework 11, for the problem session on Friday Oct. 30:
page 171: 7-1, 7-2, 7-3, 7-4, 7-6, 7-7

Homework 12, for the problem session on Friday Nov. 13:
page 199: 8-2, 8-3, 8-6, 8-9, 8-10, 8-13

Homework 13, for the problem session on Friday Nov. 20:
page 245: 9-1, 9-2, 9-3, 9-4, 9-5, 9-6, 9-7

Homework 14, for the problem session on Friday Dec. 4:
page 299: 11-1, 11-2, 11-4, 11-7, 11-13, 11-15, 11-17

## Useful books for reference:

Boothby, Introduction to Differentiable Manifolds and Riemannian Geometry - Another book about at our level

R. Narasimhan, Analysis on Real and Complex Manifolds - Very good book, though maybe somewhat advanced.

Spivak, Calculus on Manifolds - Very nice and short intro, but only does submanifolds of euclidean space, so more basic than what we are doing. Might be nice to look at for a different point of view.