Rail knotoids

Dimitrios Kodokostas; Sofia Lambropoulou

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arXiv · 1812.09493

Rail knotoids

Dimitrios Kodokostas·Sofia Lambropoulou

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Abstract

We work on the notions of rail arcs and rail isotopy in $\mathbb{R}^3$, and we introduce the notions of rail knotoid diagrams and their equivalence. Our main result is that two rail arcs in $\mathbb{R}^3$ are rail isotopic if and only if their knotoid diagram projections onto the plane of the two lines which we call rails, are equivalent. We also make a connection between the rail isotopy in $\mathbb{R}^3$ and the knot theory of the handlebody of genus $2$.

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Dimitrios Kodokostas, Sofia Lambropoulou. 2018-12-22. Rail knotoids. https://arxiv.org/abs/1812.09493

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