Lattice gauge field theory and prismatic sets

• Autores: B. Akyar, J. L. Dupont
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 108, Nº 1, 2011, págs. 26-64
• Idioma: inglés
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• Resumen

  • We study prismatic sets analogously to simplicial sets except that realization involves prisms, i.e., products of simplices rather than just simplices. Particular examples are the prismatic subdivision of a simplicial set S and the prismatic star of S. Both have the same homotopy type as S and in particular the latter we use to study lattice gauge theory in the sense of Phillips and Stone. Thus for a Lie group G and a set of parallel transport functions defining the transition over faces of the simplices, we define a classifying map from the prismatic star to a prismatic version of the classifying space of G. In turn this defines a G-bundle over the prismatic star.