MATH 227C Topics in Topology
Instructor: Emille Davie
Office: 6507 South Hall
Class Meetings: TR 12:30-1:45p BUCHN 1934
Office Hours: Wednesday 3:30-5:30
E-mail: davie (followed by @math.ucsb.edu)
Office Phone: 893-2738
Web: www.math.ucsb.edu/~davie
Text: No official text, however, online references include:
Braids: A Survey by Birman and Brendle
http://arxiv.org/pdf/math/0409205v2
Braid Groups and Artin Groups by Luis Paris
http://arxiv.org/pdf/0711.2372
Braid Groups by Kassel and Turaev
available online through Springer
An introduction to right-angled Artin groups by Ruth Charney
http://arxiv.org/pdf/math/0610668
Description:
We will start by looking at braid groups from the point of view of configuration spaces, generators and relations, mapping class groups, and as a subgroup of the automorphism group of a free group. We will also study some braid group representations including the Burau and Lawrence-Krammer representations and the Garside approach to the word and conjugacy problems for braids. The second half of the course will focus on Artin groups (a generalization of braid groups), its associated Coxeter group and their defining graphs. We will also discuss right-angled Artin (RAAGs) and Coxeter groups and the role of CAT(0) cube complexes such as the Davis and Salvetti complexes. Open research problems will be highlighted throughout.
Grading: Your grade will be based upon your attendance and participation during in-class activities.
ADA: Students with disabilities can get assistance from the Office of Services for Students with Disabilities (845-1637). I am happy to work with them and you.