Virtual strings

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2004Embargo end date: 01 Jan 2003 English Publisher:MathDoc/Centre MersenneJournal:Annales de l'Institut Fourier, volume 54, pages 2,455-2,525 (eissn: 1777-5310,

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Authors: Turaev, Vladimir;

doi: 10.5802/aif.2086 , 10.48550/arxiv.math/0310218

arXiv: math/0310218

Virtual strings

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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.

Related Organizations

French National Centre for Scientific Research
France
UNIVERSITE MARIE ET LOUIS PASTEUR
France
Institut de Recherche Mathématique Avancée
France

Keywords

General low-dimensional topology, cobordism, virtual knots, homotopy, Lie cobracket, Geometric Topology (math.GT), surfaces, skew-symmetric matrices, [PHYS.COND.CM-SCM] Physics [physics]/Condensed Matter [cond-mat]/Soft Condensed Matter [cond-mat.soft], Mathematics - Geometric Topology, 57M99, virtual strings, FOS: Mathematics, Knots and links in the \(3\)-sphere, Algebraic Topology (math.AT), Mathematics - Algebraic Topology

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