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2020 State graphs and fibered state surfaces
Darlan Girão, Jessica S Purcell
Algebr. Geom. Topol. 20(2): 987-1014 (2020). DOI: 10.2140/agt.2020.20.987

Abstract

Associated to every state surface for a knot or link is a state graph, which embeds as a spine of the state surface. A state graph can be decomposed along cut-vertices into graphs with induced planar embeddings. Associated with each such planar graph is a checkerboard surface, and each state surface is a fiber if and only if all of its associated checkerboard surfaces are fibers. We give an algebraic condition that characterizes which checkerboard surfaces are fibers directly from their state graphs. We use this to classify fibering of checkerboard surfaces for several families of planar graphs, including those associated with 2–bridge links. This characterizes fibering for many families of state surfaces.

Citation

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Darlan Girão. Jessica S Purcell. "State graphs and fibered state surfaces." Algebr. Geom. Topol. 20 (2) 987 - 1014, 2020. https://doi.org/10.2140/agt.2020.20.987

Information

Received: 18 February 2019; Revised: 16 June 2019; Accepted: 8 July 2019; Published: 2020
First available in Project Euclid: 30 April 2020

zbMATH: 07195382
MathSciNet: MR4092317
Digital Object Identifier: 10.2140/agt.2020.20.987

Subjects:
Primary: 57M25, 57M27

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.20 • No. 2 • 2020
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