^{1} Department of Mathematical Sciences, Faculty of Science, Aarhus University, Aarhus University^{2} Dokuz Eylül University^{3} Department of Mathematics, Science and Technology, Aarhus University^{4} Department of Mathematics, Science and Technology, Aarhus University

Abstract:

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.

Type:

Working paper, (pr)eprint

Language:

English

Main Research Area:

Science/technology

Publication Status:

Published

Review type:

Undetermined

Publisher:

Department of Mathematical Sciences, Aarhus University, 2008