**Math 6510 - Differentiable Manifolds**

**Fall 2013**

**Instructor:
**Ken
Bromberg

**Office:
**JWB
303

**Email:
**bromberg@math.utah.edu

**Meeting
place and time: **TTh
2:00 - 3:20, JWB
208

**Text:
**The
main text for the course is *Differential
Topology*,
by Guillemin and Pollack and some
homework will be assigned from this book. However, we will not follow
the book that closely as it treats all manifolds as subspaces of R^{n}
and we will deal with abstracts manifolds. Other books that I
recommend (in order of importance) and may refer to when planning my
lectures are *A
Comprehensive Introduction to
Differential Geometry, Vol. 1* by Spivak,
*Topology
from a Differential Viewpoint*
by Milnor and *Foundations
of Differentiable
Manifolds and Lie Groups* by Warner. All of
these books are "classics" and you should be able to find
relatively cheap used copies. However, they are not required for the
course.

**
Course description: **This
course will prepare you for the first half of Geometry/Topology
qualifying exam.

Homework:

**Final:
**The final will be a replica of the differentiable manifolds
portion of the qualifying exam. I will give it to you to do at home
at your convenience but you should do it in an hour and a half
without books and notes to best simulate the actual qualifying
exam.

**Grades: **If I believe you have a
strong chance of
passing the qualifying exam you will receive an A in the course. If
you do the homework and final but I am concerned about your chances
on the qualifying exam you will receive an A-. If you are not in
either of the first two categories your grade will be lower and based
on my discretion depending on how much work you put in the course and
how much you seem to have learned.