Normal subgroups of the braid groups and the Dehornoy ordering

The braid groups admit a left-ordering, known as the Dehornoy ordering, which has come up under many guises in recent years. I will show that normal subgroups interact with the Dehornoy ordering in such a way that 'nearly all' normal subgroups of the braid groups are densely ordered with respect to this ordering. In particular, some popular normal subgroups--such as the kernels of the Burau representations--can be easily analyzed. This is joint work with Dale Rolfsen.