Math 6510 - Differentiable Manifolds

Fall 2013

Instructor: Ken Bromberg
Office: JWB 303

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 Rn 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.

There will be regularly assigned homework some of which will be graded.

Homework 1

Homework 2

Homework 3

Homework 4

Homework 5

Homework 6     Solutions

Homework 7

Homework 8

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.