Browsing by Author "Lambropoulou, Sofia"

Now showing 1 - 3 of 3
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    Braid equivalences and the L-moves
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Lambropoulou, Sofia
    In this survey paper we present the L–moves between braids and how they can adapt and serve for establishing and proving braid equivalence theorems for various diagrammatic settings, such as for classical knots, for knots in knot complements, in c.c.o. 3–manifolds and in handlebodies, as well as for virtual knots, for flat virtuals, for welded knots and for singular knots. The L–moves are local and they provide a uniform ground for formulating and proving braid equivalence theorems for any diagrammatic setting where the notion of braid and diagrammatic isotopy is defined, the statements being first geometric and then algebraic.
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    Braidoids
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2020) Gügümcü, Neslihan; Lambropoulou, Sofia
    Braidoids generalize the classical braids and form a counterpart theory to the theory of planar knotoids, just as the theory of braids does for the theory of knots. In this paper, we introduce the notion of braidoids in R², a closure operation for braidoids, we prove an analogue of the Alexander theorem, namely an algorithm that turns a knotoid into a braidoid, and we formulate and prove a geometric analogue of the Markov theorem for braidoids using the L-moves.
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    A categorical model for the virtual braid group
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Kauffman, Louis H.; Lambropoulou, Sofia
    [no abstract available]