Generic faithfulness of the Burau representation

Stream: maths

[Ashvni Narayanan]

Hi all, I am interested in formalizing the following paper : https://arxiv.org/pdf/2209.10826.pdf
which gives conditions for faithfulness of the Burau representation for n=4. Is anybody working on the same? Also, are there others who might also be interested in this? It might require some knowledge of braids and graphs.
Thank you!

[Kim Morrison]

I'm not aware of any active work: all I can find is my suggestion that someone define the Burau representation!

I think generally this stuff should be formalizable without major difficulty, but there is a lot to be done.

Diagrammatic stuff (knots, tangles, Alexander's theorem, Markov theorem) is potentially much harder.

[Ashvni Narayanan]

Thank you! I do want to get to knots, I thought this might be a potential way of doing it.