Simplifying branched covering surface-knots by chart moves involving black vertices

Inasa Nakamura

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arXiv · 1709.07762

Simplifying branched covering surface-knots by chart moves involving black vertices

Inasa Nakamura

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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.

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Inasa Nakamura. 2017-09-21. Simplifying branched covering surface-knots by chart moves involving black vertices. https://arxiv.org/abs/1709.07762

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