On Simply Connected Quandles
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913810124636160 |
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| author | Bonatto, Marco |
| author_facet | Bonatto, Marco |
| contents | In this paper we provide an alternative characterization of finite simply connected quandles involving only cocycles with values in abelian groups of prime size. As a corollary of such a characterization and the classification of connected quandles of size $p^2$ and $p^3$ we obtain a classification of simply connected quandles of size $p^2$ (already obtained with a different method in \cite{VV}) and $p^3$ for $p>3$ using a method that works for quandles of size $p^n$ for arbitrary $n$. We also classify the simply connected quandles within two subclasses of finite involutory quandles: nilpotent latin quandles and core quandles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19109 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Simply Connected Quandles Bonatto, Marco Group Theory Geometric Topology In this paper we provide an alternative characterization of finite simply connected quandles involving only cocycles with values in abelian groups of prime size. As a corollary of such a characterization and the classification of connected quandles of size $p^2$ and $p^3$ we obtain a classification of simply connected quandles of size $p^2$ (already obtained with a different method in \cite{VV}) and $p^3$ for $p>3$ using a method that works for quandles of size $p^n$ for arbitrary $n$. We also classify the simply connected quandles within two subclasses of finite involutory quandles: nilpotent latin quandles and core quandles. |
| title | On Simply Connected Quandles |
| topic | Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2504.19109 |