Conjugacy Classes of 3-Braid Group B_3
Usman Ali

TL;DR
This paper studies the conjugacy classes in the 3-braid group B_3, identifying summit sets, minimal elements, and computing the Hilbert series, with applications to classifying knots with braid index up to three.
Contribution
It provides a detailed description of conjugacy classes in B_3, including summit sets and Hilbert series, linking algebraic properties to knot classification.
Findings
Identified summit sets in B_3
Determined smallest elements in summit sets
Computed Hilbert series for conjugacy classes
Abstract
In this article we describe the summit sets in B_3, the smallest element in a summit set and we compute the Hilbert series corresponding to conjugacy classes.The results will be related to Birman-Menesco classification of knots with braid index three or less than three.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics
