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. |
Text: |
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. |
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.