Simplifying branched covering surface-knots by an addition of 1-handles with chart loops

Abstract

A branched covering surface-knot over an oriented surface-knot $F$ is a surface-knot in the form of a branched covering over $F$. A branched covering surface-knot over $F$ is presented by a graph called a chart on a surface diagram of $F$. For a branched covering surface-knot, an addition of 1-handles equipped with chart loops is a simplifying operation which deforms the chart to the form of the union of free edges and 1-handles with chart loops. We investigate properties of such simplifications.

arXiv comment26 pages, 15 figures, title changed, minor modifications, to appear in J. Knot Theory Ramifications

References in corpus (3)

• Surface links which are coverings over the standard torus
• Satellites of an oriented surface link and their local moves
• Simplifying branched covering surface-knots by chart moves involving black vertices

Cited by in corpus (2)

• Simplifying branched covering surface-knots by chart moves involving black vertices
• Branched covering surface-knots with degree three have the simplifying numbers less than three