Mathematics > Geometric Topology
[Submitted on 22 Dec 2018 (v1), last revised 23 Mar 2019 (this version, v3)]
Title:Rail knotoids
View PDFAbstract: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 $2$.
Submission history
From: Dimitrios Kodokostas [view email][v1] Sat, 22 Dec 2018 10:09:48 UTC (41 KB)
[v2] Sat, 16 Mar 2019 10:52:07 UTC (44 KB)
[v3] Sat, 23 Mar 2019 14:43:29 UTC (46 KB)
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