Topological complexity sequences of groups
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914533243617280 |
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| author | Kishimoto, Daisuke Minowa, Yuki |
| author_facet | Kishimoto, Daisuke Minowa, Yuki |
| contents | We define the topological complexity sequence of a group as the sequence of topological complexities of its Milnor constructions. This sequence may be regarded as an intrinsic refinement of the topological complexity of a group and, unlike topological complexity itself, is meaningful for groups of infinite cohomological dimension. We show that the topological complexity sequence of every group of infinite cohomological dimension is weakly increasing and unbounded. We then estimate its growth and determine its asymptotic behavior for a finite group of even order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27514 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Topological complexity sequences of groups Kishimoto, Daisuke Minowa, Yuki Algebraic Topology 55M30, 55R35 We define the topological complexity sequence of a group as the sequence of topological complexities of its Milnor constructions. This sequence may be regarded as an intrinsic refinement of the topological complexity of a group and, unlike topological complexity itself, is meaningful for groups of infinite cohomological dimension. We show that the topological complexity sequence of every group of infinite cohomological dimension is weakly increasing and unbounded. We then estimate its growth and determine its asymptotic behavior for a finite group of even order. |
| title | Topological complexity sequences of groups |
| topic | Algebraic Topology 55M30, 55R35 |
| url | https://arxiv.org/abs/2604.27514 |