Simplicial principal bundles in parametrized spaces

Details Simplicial principal bundles in parametrized spaces Simplicial principal bundles in parametrized spaces

2012-03-12

arxiv.org/abs/1203.2460v1

Mathematics

Algebraic Topology

30 pages, uses xy-pic

Scientific paper

In this paper, motivated by recent interest in higher gauge theory, we prove that the fiberwise geometric realization functor takes a certain class of simplicial principal bundles in a suitable category of spaces over a fixed space $B$ to fiberwise principal bundles. As an application we show that the fiberwise geometric realization of the universal simplicial principal bundle for a simplicial group $G$ in the category of spaces over $B$ gives rise to a fiberwise principal bundle with structure group $|G|$. An application to classifying theory for fiberwise principal bundles is described.

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