Distributional Topological Complexity of groups
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913985063813120 |
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| author | Dranishnikov, Alexander |
| author_facet | Dranishnikov, Alexander |
| contents | We study numerical invariants $d\TC(Γ)$ and $d\cat(Γ)$ of groups recently introduced in \cite{DJ} and independently in \cite{KW}. We compute $d\TC$ for finite cyclic groups $\mathbb Z_p$ with prime $p$ as well as for nonorientable surfaces of genus $g>3$ (for orientable surfaces it was computed in \cite{DJ}). We prove the formula $$d\TC(G\ast H)=\max\{d\TC (G),d\TC (H), \cd(G\times H)\}$$ for torsion free groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03041 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distributional Topological Complexity of groups Dranishnikov, Alexander Geometric Topology We study numerical invariants $d\TC(Γ)$ and $d\cat(Γ)$ of groups recently introduced in \cite{DJ} and independently in \cite{KW}. We compute $d\TC$ for finite cyclic groups $\mathbb Z_p$ with prime $p$ as well as for nonorientable surfaces of genus $g>3$ (for orientable surfaces it was computed in \cite{DJ}). We prove the formula $$d\TC(G\ast H)=\max\{d\TC (G),d\TC (H), \cd(G\times H)\}$$ for torsion free groups. |
| title | Distributional Topological Complexity of groups |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2404.03041 |