Exact sequences of fibrations of crossed complexes, homotopy classification of maps, and nonabelian extensions of groups
| Autor: | Brown, Ronald |
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| Rok vydání: | 2008 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 10 pages, xypic, hyperref 25/06/08 version 2: 12 pages, accepted for JHRS, various minor revisions |
| Databáze: | arXiv |
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