Trisections induced by the Gluck surgery along certain spun knots

Tsukasa Isoshima; Masaki Ogawa

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arXiv · 2305.12042

Trisections induced by the Gluck surgery along certain spun knots

Tsukasa Isoshima·Masaki Ogawa

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Abstract

Gay and Meier asked whether or not a trisection diagram obtained 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 $(2n + 1, -2)$-torus knot, where $n\geq1$, and show that the trisection diagram is standard when $n = 1$. Moreover, we introduce a notion of homologically standard for trisection diagrams and show that the trisection diagram is homologically standard for all $n$.

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Tsukasa Isoshima, Masaki Ogawa. 2023-05-20. Trisections induced by the Gluck surgery along certain spun knots. https://arxiv.org/abs/2305.12042

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