Virtual strings and their cobordisms

Vladimir Turaev

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arXiv · math/0311185

Virtual strings and their cobordisms

Vladimir Turaev

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Abstract

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.

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BibTeX RIS

Vladimir Turaev. 2004-02-24. Virtual strings and their cobordisms. https://arxiv.org/abs/math/0311185

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