Higher topological complexity of Seifert fibered manifolds
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866912860208103424 |
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| author | Daundkar, Navnath Santhanam, Rekha Thandar, Soumyadip |
| author_facet | Daundkar, Navnath Santhanam, Rekha Thandar, Soumyadip |
| contents | In this article, we investigate the higher topological complexity of oriented Seifert fibered manifolds that are Eilenberg--MacLane spaces $K(G,1)$ with infinite fundamental group $G$. We first refine the cohomological lower bounds for higher topological complexity by introducing the notion of higher topological complexity weights. As an application, we show that the $r^{\text{th}}$ topological complexity of these manifolds lies in $\{3r-1, 3r, 3r+1\}$, and characterize large families where the value is $3r$ or $3r+1$. Additionally, we establish a sufficient condition for higher topological complexity to be exactly $3r$ when the base surface is orientable and aspherical. Finally, we show that the higher topological complexity of the wedge of finitely many closed, orientable, aspherical $3$-manifolds is exactly $3r+1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_01274 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Higher topological complexity of Seifert fibered manifolds Daundkar, Navnath Santhanam, Rekha Thandar, Soumyadip Algebraic Topology 55M30, 57N65, 55S99, 55P99 In this article, we investigate the higher topological complexity of oriented Seifert fibered manifolds that are Eilenberg--MacLane spaces $K(G,1)$ with infinite fundamental group $G$. We first refine the cohomological lower bounds for higher topological complexity by introducing the notion of higher topological complexity weights. As an application, we show that the $r^{\text{th}}$ topological complexity of these manifolds lies in $\{3r-1, 3r, 3r+1\}$, and characterize large families where the value is $3r$ or $3r+1$. Additionally, we establish a sufficient condition for higher topological complexity to be exactly $3r$ when the base surface is orientable and aspherical. Finally, we show that the higher topological complexity of the wedge of finitely many closed, orientable, aspherical $3$-manifolds is exactly $3r+1$. |
| title | Higher topological complexity of Seifert fibered manifolds |
| topic | Algebraic Topology 55M30, 57N65, 55S99, 55P99 |
| url | https://arxiv.org/abs/2304.01274 |