Geometry and Topology
Professor: John Etnyre
Office: 4E5
Phone: 215-898-8472
Fax: 215-573-4063
e-mail: etnyre@math.upenn.edu
Office Hours:
By appointment, I am free most of MWF and most mornings.
Lectures:
Tuesday and Thursday 12:00 to 1:30 in the David Rittenhouse Laboratory Building room 4C2.
Text Books
There is no official text for the class. I will try to make the
lectures self contained, but a few good references for the class are
- "Differential Geometry and its applications" by Oprea,
- "Riemannian Geometry: a beginner's Guide" by Morgan,
- "Differential Geometry of curves and surfaces" by DoCarmo.
Grading Policy
The course grade will be based on the following.
Homework: 60%
Final Exam: 40%
Course Content
This is
the second semester of a two semester course in topology and geometry.
This semester is an introduction to Riemannian geometry: a beautiful language
in which much of modern mathematics and physics is spoken. We will cover
- The geometry of Curves in Euclidean space,
- Manifolds in Euclidean space,
- The geometry of surfaces in Euclidean space,
- Intrinsic geometry of surfaces,
- Influences of curvature on topology.
Given time we will also discuss some (or all?) of the following topics:
- The space of metrics (Teichmueler theory),
- Minimal surfaces and surfaces of constant mean curvature (Soap bubbles),
- Analysis on surfaces,
- Higher dimensional manifolds.
Though it would be good to
have had Math 500 it is not an essential prerequisite for this course.
Anyone taking this course should have had multivariable calculus, differential
equations and linear algebra (the standard math courses at Penn through 240).
Moreover, the class will be very "proof oriented", so students should be comforable
following and producing proofs.
Check back here for more information soon.
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