On distributional topological complexity of groups and manifolds
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910159881633792 |
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| author | Dranishnikov, Alexander |
| author_facet | Dranishnikov, Alexander |
| contents | We prove the equality $\dTC(Γ)=\TC(Γ)$ for distributional topological complexity of torsion free hyperbolic and of torsion free nilpotent groups.
For the distributional topological complexity of lens spaces we prove the inequality $\dTC(L^n_p)\le 2p-1$ and for the distributional LS-category the inequality $d\cat(L^n_p)\le p-1$ which turns into equality for prime $p$ and $n>p$. We use these inequalities to bring counter-examples to the product formula for $d\cat$ and $\dTC$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16759 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On distributional topological complexity of groups and manifolds Dranishnikov, Alexander Geometric Topology Algebraic Topology Group Theory 55M30 We prove the equality $\dTC(Γ)=\TC(Γ)$ for distributional topological complexity of torsion free hyperbolic and of torsion free nilpotent groups. For the distributional topological complexity of lens spaces we prove the inequality $\dTC(L^n_p)\le 2p-1$ and for the distributional LS-category the inequality $d\cat(L^n_p)\le p-1$ which turns into equality for prime $p$ and $n>p$. We use these inequalities to bring counter-examples to the product formula for $d\cat$ and $\dTC$. |
| title | On distributional topological complexity of groups and manifolds |
| topic | Geometric Topology Algebraic Topology Group Theory 55M30 |
| url | https://arxiv.org/abs/2509.16759 |