Bounding the Kirby-Thompson invariant of spun knots
type: Item
instance of: scholarly article
title: Bounding the Kirby-Thompson invariant of spun knots
author: José Román Aranda Cuevas
author: Puttipong Pongtanapaisan
author: Scott A. Taylor
author: Suixin Zhang
published in: Algebraic \& Geometric Topology
publication date: 2024-11-04T00:00:00Z
review text: A basic context of the paper is to develop 2-knot or 4-manifold invariants using trisections. A \textit{bridge trisection} of a smooth surface in \(S^4\) is a decomposition analogous to a bridge splitting of a classical link in \(S^3\) and gives rise to the fundamental notion of the \textit{bridge number} of a knotted smooth surface in \(S^4\). \textit{R. Kirby} and \textit{A. Thompson} [Proc. Natl. Acad. Sci. USA 115, No. 43, 10857--10860 (2018; Zbl 1421.57031)] defined an invariant of a bridge trisection which measures its complexity in terms of distances between disk sets in the pants complex of the trisection surface. ``We give the first significant bound for the Kirby-Thompson invariant of spun knots. In particular, we show that the Kirby-Thompson invariant of the spun trefoil is 15.''
reviewed by: Bruno Zimmermann
Mathematics Subject Classification ID: 57K45
zbMATH DE Number: 7938174
zbMATH Keywords: bridge trisections
zbMATH Keywords: pants complex
MaRDI profile type: Publication
cites work: On the isotopy of two-dimensional surfaces in \(\mathbb{R}^4\)
cites work: Distance and bridge position
cites work: Kirby–Thompson distance for trisections of knotted surfaces
cites work: The \(\pi\)-orbifold group of a link
cites work: Q5601331
cites work: Trisecting 4-manifolds
cites work: Doubly pointed trisection diagrams and surgery on 2-knots
cites work: Q5051302
cites work: On the classification of rational tangles
cites work: A new invariant of 4-manifolds
cites work: Bridge trisections in \(\mathbb{CP}^2\) and the Thom conjecture
cites work: Symplectic 4‐manifolds admit Weinstein trisections
cites work: Reduction of bridge positions along bridge disks
cites work: Bridge trisections of knotted surfaces in 𝑆⁴
cites work: Bridge trisections of knotted surfaces in 4-manifolds
cites work: Q5698922
cites work: Bridge and pants complexities of knots
DOI: 10.2140/AGT.2024.24.3363
description: scientific article; zbMATH DE number 7938174