Kirby–Thompson distance for trisections of knotted surfaces

Publication Date

3-1-2022

Document Type

Article

Publication Title

Journal of the London Mathematical Society

Volume

105

Issue

2

DOI

10.1112/jlms.12513

First Page

765

Last Page

793

Abstract

We adapt work of Kirby–Thompson and Zupan to define an integer invariant (Formula presented.) of a bridge trisection (Formula presented.) of a smooth surface (Formula presented.) in (Formula presented.) or (Formula presented.). We show that when (Formula presented.), then the surface (Formula presented.) is unknotted. We also show that for a trisection (Formula presented.) of an irreducible surface, bridge number produces a lower bound for (Formula presented.). Consequently (Formula presented.) can be arbitrarily large.

Funding Number

DMS-1821254

Funding Sponsor

National Science Foundation

Department

Mathematics and Statistics

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