Higher topological complexity of planar polygon spaces having small genetic codes
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908510852218880 |
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| author | Datta, Sutirtha Daundkar, Navnath Sarkar, Abhishek |
| author_facet | Datta, Sutirtha Daundkar, Navnath Sarkar, Abhishek |
| contents | We study the higher (sequential) topological complexity, a numerical homotopy invariant for the planar polygon spaces. For these spaces with a small genetic codes and dimension $m$, Davis showed that their topological complexity is either $2m$ or $2m+1$. We extend these bounds to the setting of higher topological complexity. In particular, when $m$ is power of $2$, we show that the $k$-th higher topological complexity of these spaces is either $km$ or $km+1.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01529 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher topological complexity of planar polygon spaces having small genetic codes Datta, Sutirtha Daundkar, Navnath Sarkar, Abhishek Algebraic Topology 55M30, 58D29, 55R80 We study the higher (sequential) topological complexity, a numerical homotopy invariant for the planar polygon spaces. For these spaces with a small genetic codes and dimension $m$, Davis showed that their topological complexity is either $2m$ or $2m+1$. We extend these bounds to the setting of higher topological complexity. In particular, when $m$ is power of $2$, we show that the $k$-th higher topological complexity of these spaces is either $km$ or $km+1.$ |
| title | Higher topological complexity of planar polygon spaces having small genetic codes |
| topic | Algebraic Topology 55M30, 58D29, 55R80 |
| url | https://arxiv.org/abs/2412.01529 |