The Burau representation of the braid group is faithful for n = 4
In this paper we use ideas introduced earlier by Moody, Long, Long-Paton, and Bigelow to prove the theorem of the title, that the Burau representation of the classical braid group is faithful for n = 4. An immediate corollary is that the Jones representation of the braid group is also faithful for n = 4.
Summary
This research confirms the faithfulness of the Burau representation of the classical braid group for four strands, building on previous work by notable mathematicians. It also establishes that the Jones representation shares this property, providing important insights into the structure of braid groups.
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