Congruence subgroups of braid groups

Tara Brendle (University of Glasgow)

Wednesday 26th February, 2014 16:00-17:00 Maths 204


(Joint work with Dan Margalit.)  The 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.  

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