Knots and Applications

An equivalence between two theories of `non-realizable’ links

speaker: Denis Ilyutko (M.V.Lomonosov Moscow State University)

abstract: One can consider Euler tours on a connected link and construct the intersection graph corresponding to an Euler tour. There are simple graphs which are not intersection graphs for any Euler tour. Defining Reidemeister moves on intersection graphs and extending them on all graphs we obtain new theories. We show that it is enough to consider only rotating circuits, i.e. Euler tours rotating at each classical crossing and each theory of `non-realizable’ graphs is equivalent the theory constructed by using only rotating circuits. This work is partially supported by RFBR grants 10-01-00748-a.

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