Distributional Topological Complexity and LS-category

Alexander Dranishnikov; Ekansh Jauhari

doi:10.4171/esiam/4/14

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arXiv · 2401.04272

Distributional Topological Complexity and LS-category

Alexander Dranishnikov·Ekansh Jauhari

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Abstract

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 $\text{cat(X)}$.

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BibTeX RIS

Alexander Dranishnikov, Ekansh Jauhari. 2024-01-08. Distributional Topological Complexity and LS-category. https://doi.org/10.4171/esiam/4/14

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