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The quotients of the congruence subgroups of braid groups

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If you have a question about this talk, please contact Oscar Randal-Williams.

The congruence subgroups of braid groups arise from a congruence condition on the integral Burau representation B_n → GL_{n−1}(Z). We solve a problem posed by Dan Margalit, what the image of such a congruence subgroup is in GL_{n−1}(Z). We describe also the quotients of the braid groups by their congruence subgroups in terms of symplectic congruence subgroups. This is joint work with Wade Bloomquist and Nancy Scherich.

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