Combinatorial Stacks and the Four-Colour Theorem
Attal, Romain
arXiv, 0501231 / Harvested from arXiv
Text on arXiv
We 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.
Publié le : 2005-01-14
Classification:  Mathematics - Combinatorics,  Mathematical Physics,  Mathematics - Quantum Algebra 
@article{0501231,
     author = {Attal, Romain},
     title = {Combinatorial Stacks and the Four-Colour Theorem},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0501231}
}

Attal, Romain. Combinatorial Stacks and the Four-Colour Theorem. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0501231/