Simplicial principal bundles in parametrized spaces
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
Cite
@article{arxiv.1203.2460,
title = {Simplicial principal bundles in parametrized spaces},
author = {David Michael Roberts and Danny Stevenson},
journal= {arXiv preprint arXiv:1203.2460},
year = {2016}
}
Comments
v2 Corrected errors in discussion of latching objects; re-organized sections 4,5 & 6; 30 pages; uses xy-pic. v3 fixes some technical LaTeX issues preventing arrows from rendering. v4 Final version, to appear in New York J. Math