Distributional Topological Complexity and LS-category
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914939306770432 |
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| author | Dranishnikov, Alexander Jauhari, Ekansh |
| author_facet | Dranishnikov, Alexander Jauhari, Ekansh |
| contents | We define a new version of Topological Complexity (TC) of a space, denoted as $\text{dTC}$, which, we think, fits better for motion planning for some autonomous systems. Like Topological complexity, \text{dTC} is also a homotopy invariant. Also, $\text{dTC}$ has a corresponding analog, denoted as $\text{dcat}$, to the Lusternik-Schnirelmann category (cat). In this paper, we do computations and estimates for both $\text{dTC(X)}$ and $\text{dcat(X)}$ for some spaces $X$ as well as a comparison with $\text{TC(X)}$ and $\text{cat(X)}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04272 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distributional Topological Complexity and LS-category Dranishnikov, Alexander Jauhari, Ekansh Geometric Topology Algebraic Topology We define a new version of Topological Complexity (TC) of a space, denoted as $\text{dTC}$, which, we think, fits better for motion planning for some autonomous systems. Like Topological complexity, \text{dTC} is also a homotopy invariant. Also, $\text{dTC}$ has a corresponding analog, denoted as $\text{dcat}$, to the Lusternik-Schnirelmann category (cat). In this paper, we do computations and estimates for both $\text{dTC(X)}$ and $\text{dcat(X)}$ for some spaces $X$ as well as a comparison with $\text{TC(X)}$ and $\text{cat(X)}$. |
| title | Distributional Topological Complexity and LS-category |
| topic | Geometric Topology Algebraic Topology |
| url | https://arxiv.org/abs/2401.04272 |