Combinatorial Stacks and the Four-Colour Theorem

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dc.creatorAttal, Romain
dc.date2005-01-14
dc.date.accessioned2026-07-07T05:16:06Z
dc.date.available2026-07-07T05:16:06Z
dc.descriptionWe interpret the number of good four-colourings of the faces of a trivalent, spherical polyhedron as the 2-holonomy of the 2-connection of a fibered category, phi, modeled on Rep(sl(2)) and defined over the dual triangulation, T. We also build an sl(2)-bundle with connection over T, that is a global, equivariant section of phi, and we prove that the four-colour theorem is equivalent to the fact that the connection of this sl(2)-bundle vanishes nowhere. This interpretation may be a first step toward a cohomological proof of the four-colour theorem.
dc.description12 pages; uses AMS macros and xypic
dc.identifierhttps://arxiv.org/abs/math/0501231
dc.identifierhttp://arxiv.org/abs/math/0501231
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73861
dc.subjectCombinatorics
dc.subjectMathematical Physics
dc.subjectQuantum Algebra
dc.titleCombinatorial Stacks and the Four-Colour Theorem
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