Szczarba's twisting cochain is comultiplicative
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866909673465053184 |
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| author | Franz, Matthias |
| author_facet | Franz, Matthias |
| contents | We prove that Szczarba's twisting cochain is comultiplicative. In particular, the induced map from the cobar construction of the chains on a 1-reduced simplicial set X to the chains on the Kan loop group of X is a quasi-isomorphism of dg bialgebras. We also show that Szczarba's twisted shuffle map is a dgc map connecting a twisted Cartesian product with the associated twisted tensor product. This gives a natural dgc model for fibre bundles. We apply our results to finite covering spaces and to the Serre spectral sequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_08943 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Szczarba's twisting cochain is comultiplicative Franz, Matthias Algebraic Topology 55U10 (Primary), 55R20, 55T10 (Secondary) We prove that Szczarba's twisting cochain is comultiplicative. In particular, the induced map from the cobar construction of the chains on a 1-reduced simplicial set X to the chains on the Kan loop group of X is a quasi-isomorphism of dg bialgebras. We also show that Szczarba's twisted shuffle map is a dgc map connecting a twisted Cartesian product with the associated twisted tensor product. This gives a natural dgc model for fibre bundles. We apply our results to finite covering spaces and to the Serre spectral sequence. |
| title | Szczarba's twisting cochain is comultiplicative |
| topic | Algebraic Topology 55U10 (Primary), 55R20, 55T10 (Secondary) |
| url | https://arxiv.org/abs/2008.08943 |