Homotopy invariants of Gauss words

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dc.creatorGibson, Andrew
dc.date2009-01-31
dc.date2009-05-11
dc.date.accessioned2026-07-07T13:12:57Z
dc.date.available2026-07-07T13:12:57Z
dc.descriptionBy defining combinatorial moves, we can define an equivalence relation on Gauss words called homotopy. In this paper we define a homotopy invariant of Gauss words. We use this to show that there exist Gauss words that are not homotopically equivalent to the empty Gauss word, disproving a conjecture by Turaev. In fact, we show that there are an infinite number of equivalence classes of Gauss words under homotopy.
dc.description15 pages, 4 figures. Second version: added reference, corrected some comments
dc.identifierhttps://arxiv.org/abs/0902.0062
dc.identifierhttp://arxiv.org/abs/0902.0062
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/229738
dc.subjectGeometric Topology
dc.subject57M99 (Primary); 68R15 (Secondary)
dc.titleHomotopy invariants of Gauss words
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