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Rail knotoids

Dimitrios Kodokostas

Department of Mathematics, National Technical University of Athens, Zografou Campus, GR-15780 Athens, Greece

E-mail Address: dkodokostas@math.ntua.gr

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and

Sofia Lambropoulou

Department of Mathematics, National Technical University of Athens, Zografou Campus, GR-15780 Athens, Greece

E-mail Address: sofia@math.ntua.gr

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https://doi.org/10.1142/S0218216519400194Cited by:12 (Source: Crossref)

This article is part of the issue:

Special Issue: Knots, Low-Dimensional Topology and Applications — Part II

Abstract

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

Dedicated to Louis H. Kauffman for his 70th birthday

Keywords:

AMSC: 57M27, 57M25

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