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Virtual strings and their cobordisms

A virtual string is a scheme of self-intersections of a closed curve on a surface. We study algebraic invariants of strings as well as two equivalence relations on the set of strings: homotopy and cobordism. We show that the homotopy invariants of strings form an infinite dimensional Lie group. We also discuss connections between virtual strings and virtual knots.

preprint2004arXivOpen access
Vladimir Turaev
math.ATmath.GT
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Vladimir Turaev

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