Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/96365
Citations | ||
Scopus | Web of Science® | Altmetric |
---|---|---|
?
|
?
|
Type: | Journal article |
Title: | A topological fibrewise fundamental groupoid |
Author: | Roberts, D. |
Citation: | Homology, Homotopy and Applications, 2015; 17(2):37-51 |
Publisher: | International Press |
Issue Date: | 2015 |
ISSN: | 1532-0081 1532-0081 |
Statement of Responsibility: | David Michael Roberts |
Abstract: | It is well known that for certain local connectivity assumptions the fundamental groupoid of a topological space can be equipped with a topology making it a topological groupoid. In other words, the fundamental groupoid functor can be lifted through the forgetful functor from topological groupoids to groupoids. This article shows that for a map Y→X with certain relative local connectivity assumptions, the fibrewise fundamental groupoid can also be lifted to a topological groupoid over the space X. This allows the construction of a simply connected covering space in the setting of fibrewise topology, assuming a local analogue of the definition of an ex-space. When applied to maps which are up-to-homotopy locally trivial fibrations, the result is a categorified version of a covering space. The fibrewise fundamental groupoid can also be used to define a topological fundamental bigroupoid of a (suitably locally connected) topological space. |
Keywords: | fundamental groupoid; parameterised homotopy theory; topological groupoid |
Description: | This is the published version of arXiv:1411.5779 |
Rights: | Copyright status unknown |
DOI: | 10.4310/HHA.2015.v17.n2.a4 |
Grant ID: | http://purl.org/au-research/grants/arc/DP120100106 |
Published version: | http://www.intlpress.com/site/_home/index.html |
Appears in Collections: | Aurora harvest 7 Mathematical Sciences publications |
Files in This Item:
There are no files associated with this item.
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.