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math.GT2003
Virtual strings
Vladimir Turaev
A virtual string is a scheme of self-intersections of a closed curve on a surface. We introduce virtual strings and study their geometric properties and homotopy invariants. We als…
math.GT2003
Knot theory for self-indexed graphs
Matias Graña, Vladimir Turaev
We introduce and study so-called self-indexed graphs. These are (oriented) finite graphs endowed with a map from the set of edges to the set of vertices. Such graphs naturally aris…