Open Access
Fall and Winter 2017 Simplifying branched covering surface-knots by chart moves involving black vertices
Inasa Nakamura
Illinois J. Math. 61(3-4): 497-515 (Fall and Winter 2017). DOI: 10.1215/ijm/1534924837

Abstract

A branched covering surface-knot is a surface-knot in the form of a branched covering over an oriented surface-knot $F$, where we include the case when the covering has no branch points. A branched covering surface-knot is presented by a graph called a chart on a surface diagram of $F$. We can simplify a branched covering surface-knot by an addition of 1-handles with chart loops to a form such that its chart is the union of free edges and 1-handles with chart loops. We investigate properties of such simplifications for the case when branched covering surface-knots have a non-zero number of branch points, using chart moves involving black vertices.

Citation

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Inasa Nakamura. "Simplifying branched covering surface-knots by chart moves involving black vertices." Illinois J. Math. 61 (3-4) 497 - 515, Fall and Winter 2017. https://doi.org/10.1215/ijm/1534924837

Information

Received: 3 October 2017; Revised: 10 April 2018; Published: Fall and Winter 2017
First available in Project Euclid: 22 August 2018

zbMATH: 06932514
MathSciNet: MR3845731
Digital Object Identifier: 10.1215/ijm/1534924837

Subjects:
Primary: 57Q45
Secondary: 57Q35

Rights: Copyright © 2017 University of Illinois at Urbana-Champaign

Vol.61 • No. 3-4 • Fall and Winter 2017
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