The deviating subgroup conjecture for the Burau representation of $B_3$

Let $F$ be the deviating subgroup associated with the image of the Burau representation of $B_3$, and let a group be free of countably infinite rank when it has a countably infinite free basis. Deviating subgroup conjecture. The deviating subgroup $F$ is free of countably infinite rank. The paper proves that $F$ has free rank at least $9$ and establishes that it is nontrivial; the conjecture predicts the exact infinite-rank structure of this subgroup. The surrounding discussion connects the analysis of $F$ with the still-open faithfulness problem for the Burau representation of $B_4$.