Secondary cohomology operations and the loop space cohomology
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916583341817856 |
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| author | Saneblidze, Samson |
| author_facet | Saneblidze, Samson |
| contents | Motivated by the loop space cohomology we construct the secondary operations on the cohomology $H^*(X; \mathbb{Z}_p)$ to be a Hopf algebra for a simply connected space $X.$ The loop space cohomology ring $H^*(ΩX; \mathbb{Z}_p)$ is calculated in terms of generators and relations. This answers to A. Borel's decomposition of a Hopf algebra into a tensor product of the monogenic ones in which the heights of generators are determined by means of the action of the primary and secondary cohomology operations on $H^*(X;\mathbb{Z}_p).$ An application for calculating of the loop space cohomology of the exceptional group $F_4$ is given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04861 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Secondary cohomology operations and the loop space cohomology Saneblidze, Samson Algebraic Topology 55S20 (primary) 55P35, 55N10 (secondary) Motivated by the loop space cohomology we construct the secondary operations on the cohomology $H^*(X; \mathbb{Z}_p)$ to be a Hopf algebra for a simply connected space $X.$ The loop space cohomology ring $H^*(ΩX; \mathbb{Z}_p)$ is calculated in terms of generators and relations. This answers to A. Borel's decomposition of a Hopf algebra into a tensor product of the monogenic ones in which the heights of generators are determined by means of the action of the primary and secondary cohomology operations on $H^*(X;\mathbb{Z}_p).$ An application for calculating of the loop space cohomology of the exceptional group $F_4$ is given. |
| title | Secondary cohomology operations and the loop space cohomology |
| topic | Algebraic Topology 55S20 (primary) 55P35, 55N10 (secondary) |
| url | https://arxiv.org/abs/2409.04861 |