The Slope Conjecture for 3-String Montesinos Knots
Xudong Leng, Zhiqing Yang, Ximin Liu
TL;DR
This paper verifies the Slope Conjecture and Strong Slope Conjecture for a class of 3-string Montesinos knots, linking polynomial degrees to essential surfaces in their complements.
Contribution
It provides the first verification of these conjectures for 3-string Montesinos knots under specific conditions.
Findings
Confirmed the Slope Conjecture for these knots
Confirmed the Strong Slope Conjecture for these knots
Established a connection between polynomial degrees and essential surfaces
Abstract
The (Strong) Slope Conjecture relates the degree of the colored Jones polynomial of a knot to certain essential surfaces in the knot complement. We verify the Slope Conjecture and the Strong Slope Conjecture for 3-string Montesinos knots satisfying certain conditions.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology