Rail knotoids
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS(2019)
摘要
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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关键词
Rail arc, rail isotopy, rail knotoid diagram, rail equivalence, rail knotoid, knot, knot invariant
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