Equal sized hyperbolic fish from M. C. Escher

Math 537B Spring 2006
Room/Time: Tuesday, Thursday 12:301:45 in Math East 246
Instructor: David Glickenstein
Office: Mathematics 213
Office Phone: 6212463
Email:glickenstein@math.arizona.edu
Presentations on May 4
Presentations will be given May 4 (Dead Day) in Math 320 1pm to 5pm (if it takes that long).
Syllabus summary
We will begin by finishing Lee's book, Chapters 711. After that, we will
explore one or more of the following topics: Geometrization of
threemanifolds, Laplacian comparison, Bishop comparison theorem, the
sphere theorem, Gromov's compactness theorem, Cheeger's finiteness theorem.
Printed resources
The books we are currently using are:
Other books of note:
Homework assignments
Lecture notes
These lecture notes are not particularly well edited and not for general
distribution, which is why the files are password protected.
Possible project topics
The following are possible project topics. Please talk with me about the
scope of the work. You are also welcome to suggest other topics.
 Simplectic geometry
 Spherical and hyperbolic trigonometry
 Hodge theorem
 Finsler geometry
 Nonlinear averaging and center of mass
 Moduli space of flat metrics
 Frobenius theorem
 Grassmannians
 Bochner technique
 Riemannian submersions
 ChernGaussBonnet theorem
 Morse Index Theorem
Last updated May 2, 2006