Adams' cobar construction as a monoidal $E_{\infty}$-coalgebra model of the based loop space
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866910449973329920 |
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| author | Medina-Mardones, Anibal M. Rivera, Manuel |
| author_facet | Medina-Mardones, Anibal M. Rivera, Manuel |
| contents | We prove that the classical map comparing Adams' cobar construction on the singular chains of a pointed space and the singular cubical chains on its based loop space is a quasi-isomorphism preserving explicitly defined monoidal $E_\infty$-coalgebra structures. This contribution extends to its ultimate conclusion a result of Baues, stating that Adams' map preserves monoidal coalgebra structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_02790 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Adams' cobar construction as a monoidal $E_{\infty}$-coalgebra model of the based loop space Medina-Mardones, Anibal M. Rivera, Manuel Algebraic Topology 57T30, 55P35, 18N70, 55U10, 55N45, 55S05 We prove that the classical map comparing Adams' cobar construction on the singular chains of a pointed space and the singular cubical chains on its based loop space is a quasi-isomorphism preserving explicitly defined monoidal $E_\infty$-coalgebra structures. This contribution extends to its ultimate conclusion a result of Baues, stating that Adams' map preserves monoidal coalgebra structures. |
| title | Adams' cobar construction as a monoidal $E_{\infty}$-coalgebra model of the based loop space |
| topic | Algebraic Topology 57T30, 55P35, 18N70, 55U10, 55N45, 55S05 |
| url | https://arxiv.org/abs/2108.02790 |