Trisections induced by the Gluck surgery along certain spun knots

Abstract

Gay and Meier asked whether or not a trisection diagram constructed by the Gluck twist on a spun or a twist spun 2-knot obtained from some method is standard. In this paper, we depict the trisection diagrams explicitly when the 2-knot is the spun [Formula: see text]-torus knot, where [Formula: see text], and show that the trisection diagram is standard when [Formula: see text]. Moreover, we introduce a notion of homologically standard for trisection diagrams and show that the trisection diagram is homologically standard for all [Formula: see text].