MATH 7590 Geometric Topology

Fall 2003

Course Information

Course: MATH 7590 Geometric Topology
Time and Place: Tuesday & Thursday, 10:30 am - 12:00 noon, in 113 Lockett
Instructor: Dan Cohen
Office Hours: tentatively Monday, Wednesday, Friday, 1:40 - 2:30 pm, in 372 Lockett,
and by appointment
Prerequisites: The exposure to the fundamental group and covering spaces provided by MATH 7512 Topology II
Grade: Based on homework and an in-class presentation.
Some homework problems and potential presentation topics are posted here.
There will be no formal textbook for this course.
Much of the subject matter may be found in Moran's book "The Mathematical Theory of Knots and Braids"
This and other potential sources for material covered in this course are listed here.

Course Description

The course will be a broad survey of selected current research areas in topology within our Department, such as Braid Theory, Arrangements, 3-manifolds, Complements of Knots and Links, and Mapping Class Groups of 2-manifolds. The focus, at least initially, will be on braid groups.

Concepts from geometric topology/group theory will be explored in the contexts of these subjects. These include aspects of infinite group theory such as the lower central series, word and conjugacy problems, Fox calculus, etc.. Other (related) topics include braid group representations and classical knot and link invariants (e.g., Alexander polynomials). The course will also provide an introduction to configuration spaces and selected generalizations, and connections to subjects such as combinatorics and the theory of reflection groups.

Department of Mathematics
Louisiana State University
Baton Rouge, LA, 70803
Office: 372 Lockett
Phone: (225) 578-1576