The loop group and the cobar construction
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2009
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| _version_ | 1866914944995295232 |
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| author | Hess, Kathryn Tonks, Andrew |
| author_facet | Hess, Kathryn Tonks, Andrew |
| contents | We prove that for any 1-reduced simplicial set X, Adams' cobar construction, ΩCX, on the normalised chain complex of X is naturally a strong deformation retract of the normalised chains CGX on the Kan loop group GX, opening up the possibility of applying the tools of homological algebra to transfering perturbations of algebraic structure from the latter to the former. In order to prove our theorem, we extend the definition of the cobar construction and actually obtain the existence of such a strong deformation retract for all 0-reduced simplicial sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0903_1651 |
| institution | arXiv |
| publishDate | 2009 |
| record_format | arxiv |
| spellingShingle | The loop group and the cobar construction Hess, Kathryn Tonks, Andrew Algebraic Topology 55P35 (Primary), 16W30, 18G30, 55U10, 57T05, 57T30 (Secondary) We prove that for any 1-reduced simplicial set X, Adams' cobar construction, ΩCX, on the normalised chain complex of X is naturally a strong deformation retract of the normalised chains CGX on the Kan loop group GX, opening up the possibility of applying the tools of homological algebra to transfering perturbations of algebraic structure from the latter to the former. In order to prove our theorem, we extend the definition of the cobar construction and actually obtain the existence of such a strong deformation retract for all 0-reduced simplicial sets. |
| title | The loop group and the cobar construction |
| topic | Algebraic Topology 55P35 (Primary), 16W30, 18G30, 55U10, 57T05, 57T30 (Secondary) |
| url | https://arxiv.org/abs/0903.1651 |