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arXiv · 2204.03907

On the considerations adopted by Breidze and Traczyk towards the faithfulness of Burau representation for $n=4$

Rawia A. Jinani·Mohammad N. Abdulrahim
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Abstract

This work discusses the open problem of the faithfulness of the reduced Burau representation for $n=4$. Birman showed that in order to prove this representation is faithful, it is sufficient to find two matrices $A$ and $B$ that generate a free group of rank 2. Breidze and Traczyk proved that $A^{3}$ and $B^{3}$ generate the free group of rank 2. In our work, we show that $A^{2}$ and $B^{2}$ generate the free group of rank 2.

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Rawia A. Jinani, Mohammad N. Abdulrahim. 2022-12-28. On the considerations adopted by Breidze and Traczyk towards the faithfulness of Burau representation for $n=4$. https://arxiv.org/abs/2204.03907

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