On the topological complexity of non-simply connected spaces
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908876184485888 |
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| author | Minowa, Yuki |
| author_facet | Minowa, Yuki |
| contents | Topological complexity is a numerical homotopy invariant that measures the instability of motion planning in a space. To study the topological complexity of non-simply connected spaces, Costa and Farber introduced a cohomology class whose nilpotency gives a lower bound of topological complexity. Farber and Mescher constructed a spectral sequence that evaluates this nilpotency without direct computation. We extend these results with respect to a group homomorphism. As an application, we determine the topological complexity of some 3-manifolds with nonabelian fundamental group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09407 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the topological complexity of non-simply connected spaces Minowa, Yuki Algebraic Topology 55M30 Topological complexity is a numerical homotopy invariant that measures the instability of motion planning in a space. To study the topological complexity of non-simply connected spaces, Costa and Farber introduced a cohomology class whose nilpotency gives a lower bound of topological complexity. Farber and Mescher constructed a spectral sequence that evaluates this nilpotency without direct computation. We extend these results with respect to a group homomorphism. As an application, we determine the topological complexity of some 3-manifolds with nonabelian fundamental group. |
| title | On the topological complexity of non-simply connected spaces |
| topic | Algebraic Topology 55M30 |
| url | https://arxiv.org/abs/2603.09407 |