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
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
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