4-Strand Burau is Unfaithful Modulo 5
Joel Gibson, Geordie Williamson, Oded Yacobi
TL;DR
The paper presents a new algorithm leveraging reservoir sampling to find kernel elements in the 4-strand Burau representation modulo 5, demonstrating unfaithfulness of the representation.
Contribution
It introduces a novel algorithm for detecting kernel elements in the Burau representation, specifically applied to 4-strands modulo 5, revealing unfaithfulness.
Findings
Explicit kernel element found in 4-strand Burau modulo 5
Demonstrates unfaithfulness of the Burau representation in this case
Introduces a new sampling-based algorithm for kernel detection
Abstract
We introduce a new algorithm for finding kernel elements in the Burau representation. Our algorithm applies reservoir sampling to a statistic on matrices which is closely correlated with Garside length. Using this we exhibit an explicit kernel element in the Burau representation on 4-strands reduced modulo 5.
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Taxonomy
TopicsAnomaly Detection Techniques and Applications · Seismic Imaging and Inversion Techniques · Topological and Geometric Data Analysis