Exact sequences of fibrations of crossed complexes, homotopy classification of maps, and nonabelian extensions of groups
| dc.creator | Brown, Ronald | |
| dc.date | 2008-02-29 | |
| dc.date | 2008-06-25 | |
| dc.date.accessioned | 2026-07-07T09:46:18Z | |
| dc.date.available | 2026-07-07T09:46:18Z | |
| dc.description | The classifying space of a crossed complex generalises the construction of Eilenberg-Mac Lane spaces. We show how the theory of fibrations of crossed complexes allows the analysis of homotopy classes of maps from a free crossed complex to such a classifying space. This gives results on the homotopy classification of maps from a CW-complex to the classifying space of a crossed module and also, more generally, of a crossed complex whose homotopy groups vanish in dimensions between 1 and n. The results are analogous to those for the obstruction to an abstract kernel in group extension theory. | |
| dc.description | 10 pages, xypic, hyperref 25/06/08 version 2: 12 pages, accepted for JHRS, various minor revisions | |
| dc.identifier | https://arxiv.org/abs/0802.4357 | |
| dc.identifier | http://arxiv.org/abs/0802.4357 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163483 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Category Theory | |
| dc.subject | 13D02,18G50,20J05,55S37,55S45 | |
| dc.title | Exact sequences of fibrations of crossed complexes, homotopy classification of maps, and nonabelian extensions of groups | |
| dc.type | text |