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Two complete invariants of oriented knots
Dimitrios Kodokostas
We construct two complete invariants of oriented classical knots in space. The value of each invariant on any knot is a set, infinite for the first invariant and finite for the sec…
Knot invariants for rail knotoids
Dimitrios Kodokostas, Sofia Lambropoulou
To each rail knotoid we associate two unoriented knots along with their oriented counterparts, thus deriving invariants for rail knotoids based on these associations. We then trans…
Rail knotoids
Dimitrios Kodokostas, Sofia Lambropoulou
We work on the notions of rail arcs and rail isotopy in , and we introduce the notions of rail knotoid diagrams and their equivalence. Our main result is that two rai…
A spanning set and potential basis of the mixed Hecke algebra on two fixed strands
Dimitrios Kodokostas, Sofia Lambropoulou
The mixed braid groups , with two fixed strands and moving ones, are known to be related to the knot theory of certain families of -manifolds. I…