Mathematics 139 - Classical Geometry and Low-Dimensional Topology; Spring 2001

Instructor: Danny Calegari 432 Science Center

Course Assistant: Kathy Paur 321b Science Center

Description of course

A continuation of the study of spherical, Euclidean and especially hyperbolic geometry in two and three dimensions begun in Mathematics 138. The emphasis will be on the relationship with topology, and the existence of metrics of constant curvature on a vast class of two and three dimensional manifolds.

We will concentrate mainly on a detailed study of examples, and we will try to be as explicit and as elementary as possible. Topics to be covered might include: uniformization for surfaces, shapes and volumes of hyperbolic polyhedra, circle packing and Andreev's theorem, and hyperbolic structures on knot complements.

Available for download

The final exam was posted on this website at noon on Wednesday, May 9th, and is due in my mailbox at 3pm on Tuesday, May 15th.

Answers to homework problems should take the form of complete sentences. It's important not merely to find the solution to a problem but also to communicate that solution effectively.

Recommended texts for course

Useful for extra reading

last updated: 16th March 2001

If you have any comments on the material in this page, or if you wish to comment on the material in the course, contact Danny Calegari via email. The image to the right is a symmetric tiling of Euclidean 3-space. It is a still from the video Not Knot produced by the (now defunct) Geometry Center.

Danny Calegari's home page