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Type: Journal article
Title: Simplicial principal bundles in parametrized spaces
Author: Roberts, D.
Stevenson, D.
Citation: New York Journal of Mathematics, 2016; 22:405-440
Publisher: University of Albany
Issue Date: 2016
ISSN: 1076-9803
Statement of
David M. Roberts, Danny Stevenson
Abstract: In this paper we study the classifying theory of principal bundles in the parametrized setting, motivated by recent interest in higher gauge theory. Using simplicial techniques, we construct a product-preserving classifying space functor for groups in the category of spaces over a fixed space B. Additionally, we prove that the fiberwise geometric realization functor sends a large class of simplicial parametrized principal bundles to ordinary parametrized 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 parametrized principal bundle with structure group |G|.
Keywords: Simplicial principal bundles; parametrized homotopy theory; classifying spaces; parametrized groups
Description: Published April 21, 2016
Rights: © authors retains copyright
RMID: 0030047114
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Appears in Collections:Mathematical Sciences publications

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