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arXiv · 1701.04496

Classification of Minimal Separating Sets in Low Genus Surfaces

J. J. P. Veerman·William J. Maxwell·Victor Rielly·Austin K. Williams
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Abstract

Consider a surface $S$ and let $M\subset S$. If $S\setminus M$ is not connected, then we say $M$ \emph{separates} $S$, and we refer to $M$ as a \emph{separating set} of $S$. If $M$ separates $S$, and no proper subset of $M$ separates $S$, then we say $M$ is a \emph{minimal separating set} of $S$. In this paper we use methods of computational combinatorial topology to classify the minimal separating sets of the orientable surfaces of genus $g=2$ and $g=3$. The classification for genus 0 and 1 was done in earlier work, using methods of algebraic topology.

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J. J. P. Veerman, William J. Maxwell, Victor Rielly, Austin K. Williams. 2017-01-17. Classification of Minimal Separating Sets in Low Genus Surfaces. https://arxiv.org/abs/1701.04496

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