The strong slope conjecture for cablings and connected sums
Kenneth L Baker, Kimihiko Motegi, Toshie Takata
TL;DR
This paper proves that the Strong Slope Conjecture remains valid under connect sums and cabling operations, and confirms it for graph knots, advancing understanding in knot theory.
Contribution
It demonstrates the preservation of the Strong Slope Conjecture under connect sums and cabling, and verifies it for a class of graph knots.
Findings
Strong Slope Conjecture is closed under connect sums and cabling
Established the conjecture for graph knots
Provides technical conditions for the conjecture's stability
Abstract
We show that, under some technical conditions, the Strong Slope Conjecture proposed by Kalfagianni and Tran is closed under connect sums and cabling. As an application, we establish the Strong Slope Conjecture for graph knots.
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Taxonomy
TopicsGeometric and Algebraic Topology · Limits and Structures in Graph Theory · Algebraic Geometry and Number Theory