Faithfulness of the Lawrence representation of braid groups
Hao Zheng

TL;DR
This paper proves that the Lawrence representation of braid groups is faithful for all parameters m greater than or equal to 2, enhancing understanding of braid group representations.
Contribution
It establishes the faithfulness of the Lawrence representation for all m ≥ 2, extending previous results and connecting it to well-known braid group representations.
Findings
Lawrence representation is faithful for m ≥ 2
Special cases include reduced Burau and Lawrence-Krammer representations
Provides new insights into braid group representations
Abstract
The Lawrence representation is a family of homological representation of the braid group , which specializes to the reduced Burau and the Lawrence-Krammer representation when is 1 and 2. In this article we show that the Lawrence representation is faithful for .
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics
