Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/102319
Type: | Journal article |
Title: | Simplicial principal bundles in parametrized spaces |
Author: | Roberts, D. Stevenson, D. |
Citation: | The New York Journal of Mathematics, 2016; 22:405-440 |
Publisher: | University of Albany |
Issue Date: | 2016 |
ISSN: | 1076-9803 1076-9803 |
Statement of Responsibility: | 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 |
Grant ID: | http://purl.org/au-research/grants/arc/DP120100106 |
Published version: | http://nyjm.albany.edu/j/2016/22-19v.pdf |
Appears in Collections: | Aurora harvest 3 Mathematical Sciences publications |
Files in This Item:
File | Description | Size | Format | |
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hdl_102319.pdf | Published version | 500.57 kB | Adobe PDF | View/Open |
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