On the sequential topological complexity of group homomorphisms
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913238392766464 |
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| author | Kuanyshov, Nursultan |
| author_facet | Kuanyshov, Nursultan |
| contents | We define and develop a homotopy invariant notion for the sequential topological complexity of a map $f:X\to Y,$ denoted $TC_{r}(f)$, that interacts with $TC_{r}(X)$ and $TC_{r}(Y)$ in the same way Jamie Scott's topological complexity map $TC(f)$ interacts with $TC(X)$ and $TC(Y).$ Furthermore, we apply $TC_{r}(f)$ to studying group homomorphisms $ϕ: Γ\to Λ.$
In addition, we prove that the sequential topological complexity of any nonzero homomorphism of a torsion group cannot be finite. Also, we give the characterisation of cohomological dimension of group homomorphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13389 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the sequential topological complexity of group homomorphisms Kuanyshov, Nursultan Algebraic Topology Group Theory Primary 50M30, Secondary 20J06, 20K45, 20K30, 20K10 We define and develop a homotopy invariant notion for the sequential topological complexity of a map $f:X\to Y,$ denoted $TC_{r}(f)$, that interacts with $TC_{r}(X)$ and $TC_{r}(Y)$ in the same way Jamie Scott's topological complexity map $TC(f)$ interacts with $TC(X)$ and $TC(Y).$ Furthermore, we apply $TC_{r}(f)$ to studying group homomorphisms $ϕ: Γ\to Λ.$ In addition, we prove that the sequential topological complexity of any nonzero homomorphism of a torsion group cannot be finite. Also, we give the characterisation of cohomological dimension of group homomorphisms. |
| title | On the sequential topological complexity of group homomorphisms |
| topic | Algebraic Topology Group Theory Primary 50M30, Secondary 20J06, 20K45, 20K30, 20K10 |
| url | https://arxiv.org/abs/2402.13389 |