Congruence subgroups of braid groups

Geometry Topology Seminar
Monday, September 23, 2013 - 15:05
1 hour (actually 50 minutes)
Skiles 006
U Glasgow
The so-called integral Burau representation gives a symplectic representation of the braid group.  In this talk we will discuss the resulting congruence subgroups of braid groups, that is, preimages of the principal congruence subgroups of the symplectic group.  In particular, we will show that the level 4 congruence braid group is equal to the group generated by squares of Dehn twists.  One key tool is a "squared lantern relation" amongst Dehn twists. Joint work with Dan Margalit.