On spaces of minimal higher topological complexity
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913470578950144 |
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| author | Rudyak, Yuli |
| author_facet | Rudyak, Yuli |
| contents | Let TC$_n$(X) denote the n-th topological complexity of a topological space X. It is known that TC$_n$(X) does not exceed n-1 for non-contractible X, and so it makes sense to describe spaces X with TC$_n$(X) =n-1. Grant--Lupton--Oprea proved the following: If X is a nilpotent space with TC$_n$(X)=n-1 then X is homotopy equivalent to an odd-dimensional sphere. Here we made an attempt to get rid of nilpotency condition and prove the following: If TC$_n$(X) =n-1 then either X is homotopy equivalent to a sphere of odd dimension or is a homology circle with the infinite cyclic fundamental group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07364 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On spaces of minimal higher topological complexity Rudyak, Yuli Algebraic Topology 55M30, 55S40 Let TC$_n$(X) denote the n-th topological complexity of a topological space X. It is known that TC$_n$(X) does not exceed n-1 for non-contractible X, and so it makes sense to describe spaces X with TC$_n$(X) =n-1. Grant--Lupton--Oprea proved the following: If X is a nilpotent space with TC$_n$(X)=n-1 then X is homotopy equivalent to an odd-dimensional sphere. Here we made an attempt to get rid of nilpotency condition and prove the following: If TC$_n$(X) =n-1 then either X is homotopy equivalent to a sphere of odd dimension or is a homology circle with the infinite cyclic fundamental group. |
| title | On spaces of minimal higher topological complexity |
| topic | Algebraic Topology 55M30, 55S40 |
| url | https://arxiv.org/abs/2402.07364 |