On addition of 1-handles with chart loops to 2-dimensional braids

Inasa Nakamura

doi:10.1142/s0218216516500619

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arXiv · 1503.00404

On addition of 1-handles with chart loops to 2-dimensional braids

Inasa Nakamura

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Abstract

A 2-dimensional braid over an oriented surface-knot $F$ is presented by a graph called a chart on a surface diagram of $F$. We consider 2-dimensional braids obtained by an addition of 1-handles equipped with chart loops. We introduce moves of 1-handles with chart loops, called 1-handle moves, and we investigate how much we can simplify a 2-dimensional braid by using 1-handle moves. Further, we show that an addition of 1-handles with chart loops is an unbraiding operation.

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Inasa Nakamura. 2016-07-01. On addition of 1-handles with chart loops to 2-dimensional braids. https://doi.org/10.1142/s0218216516500619

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