Math 7590, Mapping Class Groups
T Th 9:10-10:30
135 Lockett
Spring 2007
· Professor: Tara E. Brendle
· Office: Lockett 254
· Office Hours: T Th 10:30 – 11:30
· E-mail: brendle@math.lsu.edu
· Phone: 578-1657
Prerequisite: Math 7510 or equivalent
Course Description: This course will serve as an
introduction to mapping class groups of surfaces. Mapping class groups are a
fundamental object of study in topology, as the automorphism groups of
2-manifolds, but also arise naturally in many other fields, such as complex
analysis and algebraic geometry. We will survey some basics such as generators
and relations for the mapping class group, subgroups important in 3-manifold
theory such as the Torelli group and the handlebody subgroup, and
representations of mapping class groups. As time permits, and according to the
interests of the class, we will also discuss related groups in geometric group
theory, Teichmuller theory, and associated combinatorial structures such as the
curve complex, among other topics.
Text: Farb and Margalit, A Primer on Mapping Class Groups. This is a manuscript in preparation. See Prof. Brendle for information on how to obtain a copy and how to register for the “Primer on MCGs” mailing list.
Additional Resources: As the semester progresses, I will be listing on the course webpage other texts and papers which you may find useful as supplementary material. Click here to see the list: List of Some Additional References
Assessment: Each
student will be required to give at least one class presentation during the
course of the semester.
Assessment will be based on preparation for and delivery of this
presentation, as well as on observed effort and engagement with the course
during the semester.
Homework: Homework problems will be assigned regularly in class
throughout the semester. The
purpose of these exercises is to help the student engage with the material and
to practice the techniques and concepts learned in the course. Homework problems will not be collected,
but students are encouraged to stop by office hours to discuss them.