1 Department of Mathematical Sciences, Faculty of Science, Aarhus University, Aarhus University2 Dokuz Eylül University3 Department of Mathematics, Science and Technology, Aarhus University4 Department of Mathematics, Science and Technology, Aarhus University
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 and the prismatic star of . Both have the same homotopy type as and in particular the latter we use to study lattice gauge theory in the sense of Phillips and Stone. Thus for a Lie group 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 . In turn this defines a -bundle over the prismatic star.
Working paper, (pr)eprint
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Department of Mathematical Sciences, Aarhus University, 2008