The trunk number of satellite knots and Thurston norm

2023/07/02 by Zehan Pan, Pan, Zehan
Mathematics · Engineering · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Advanced Materials and Mechanics

paper · pdf · doi:10.48550/arxiv.2311.02514

Abstract

Assume J ⊂ℝ³ is a non-trivial knot, and assume k⊂ S¹× D² is a satellite pattern. Let N be the generalized Thurston norm of the homology class of the meridian disk in S¹× D² with respect to k. Let K be the satellite knot of J with pattern k. We show that the trunk number of K is strictly greater than N times the trunk number of J.

Related

• A lower bound on the width of satellite knots
• Augmentation Rank of Satellites with Braid Pattern
• Waist and trunk of knots
• Extending Van Cott's bounds for the τ-invariant of satellite knots
• On wrapping number, adequacy and the crossing number of satellite knots