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

Inasa Nakamura

doi:10.1142/s0218216518500311

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arXiv · 1707.07888

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

Inasa Nakamura

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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.

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Inasa Nakamura. 2018-02-27. Simplifying branched covering surface-knots by an addition of 1-handles with chart loops. https://doi.org/10.1142/s0218216518500311

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