Categorifying Coloring Numbers

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dc.creatorArmstrong, John
dc.date2008-03-11
dc.date.accessioned2026-07-07T09:26:12Z
dc.date.available2026-07-07T09:26:12Z
dc.descriptionColoring numbers are one of the simplest combinatorial invariants of knots and links to describe. And with Joyce's introduction of quandles, we can understand them more algebraically. But can we extend these invariants to tangles -- knots and links with free ends? Indeed we can, once we categorify. Starting from the definition of coloring numbers, we will categorify them and establish this extension to tangles. Then, decategorifying will leave us with matrix representations of the monoidal category of tangles.
dc.descriptionTo appear in "Interactions between Representation Theory, Quantum Field Theory, Category Theory, and Quantum Information Theory" conference proceedings
dc.identifierhttps://arxiv.org/abs/0803.1642
dc.identifierhttp://arxiv.org/abs/0803.1642
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/156671
dc.subjectGeometric Topology
dc.subjectCategory Theory
dc.subject57M27; 57M99; 18B99
dc.titleCategorifying Coloring Numbers
dc.typetext

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