Infinitely many standard trisection diagrams for Gluck twisting

TL;DR

This paper proves that the trisection diagram for the Gluck twist on spun (p+1,p)-torus knots in S^4 is standard for all integers p ≥ 2, confirming a specific case of a broader question.

Contribution

It demonstrates that the trisection diagram for the Gluck twist on spun (p+1,p)-torus knots is standard for all p ≥ 2, providing an infinite family of standard diagrams.

Findings

The trisection diagram for the Gluck twist on spun (p+1,p)-torus knots is standard.

The result applies to all integers p ≥ 2.

It affirms a specific case of Gay and Meier's question.

Abstract

Gay and Meier asked if a trisection diagram for the Gluck twist on a spun or twist-spun 2-knot in $S^4$ obtained by a certain method is standard. In this paper, we show that the trisection diagram for the Gluck twist on the spun $(p+1,p)$-torus knot is standard, where $p$ is any integer greater than or equal to 2.