TOWARDS A 2-DIMENSIONAL NOTION OF HOLONOMY
| dc.contributor.author | BROWN, R. O. N. A. L. D. | |
| dc.contributor.author | ICEN, I. L. H. A. N. | |
| dc.date.accessioned | 2024-08-04T20:52:07Z | |
| dc.date.available | 2024-08-04T20:52:07Z | |
| dc.date.issued | 2022 | |
| dc.department | İnönü Üniversitesi | en_US |
| dc.description.abstract | Previous work (Pradines, C.R. Acad. Sci. Paris 263 (1966) 907, Aof and Brown, Topology Appl. 47 (1992) 97) has given a setting for a holonomy Lie groupoid of a locally Lie groupoid. Here we develop analogous 2-dimensional notions starting from a locally Lie crossed module of groupoids. This involves replacing the Ehresmann notion of a local smooth coadmissible section of a groupoid by a local smooth coadmissible homotopy (or free derivation) for the crossed module case. The development also has to use corresponding notions for certain types of double groupoids. This leads to a holonomy Lie groupoid rather than double groupoid, but one which involves the 2-dimensional information. | en_US |
| dc.identifier.doi | 10.3934/jgm.2022011 | |
| dc.identifier.endpage | 357 | en_US |
| dc.identifier.issn | 1941-4889 | |
| dc.identifier.issn | 1941-4897 | |
| dc.identifier.issue | 2 | en_US |
| dc.identifier.scopus | 2-s2.0-85133442053 | en_US |
| dc.identifier.scopusquality | Q3 | en_US |
| dc.identifier.startpage | 331 | en_US |
| dc.identifier.uri | https://doi.org/10.3934/jgm.2022011 | |
| dc.identifier.uri | https://hdl.handle.net/11616/100768 | |
| dc.identifier.volume | 14 | en_US |
| dc.identifier.wos | WOS:000809583000001 | en_US |
| dc.identifier.wosquality | Q4 | en_US |
| dc.indekslendigikaynak | Web of Science | en_US |
| dc.indekslendigikaynak | Scopus | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | Amer Inst Mathematical Sciences-Aims | en_US |
| dc.relation.ispartof | Journal of Geometric Mechanics | en_US |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | Crossed module | en_US |
| dc.subject | homotopy | en_US |
| dc.subject | double groupoid | en_US |
| dc.subject | linear section | en_US |
| dc.subject | Lie groupoids | en_US |
| dc.subject | holonomy | en_US |
| dc.title | TOWARDS A 2-DIMENSIONAL NOTION OF HOLONOMY | en_US |
| dc.type | Article | en_US |
