Higher Analogues of Discrete Topological Complexity

Hilal Alabay; Ayse Borat; Esra Cihangirli; Esma Dirican Erdal

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arXiv · 2310.01333

Higher Analogues of Discrete Topological Complexity

Hilal Alabay·Ayse Borat·Esra Cihangirli·Esma Dirican Erdal

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Abstract

In this paper, we introduce the n-th discrete topological complexity and study its properties such as its relation with simplicial Lusternik-Schnirelmann category and how the higher dimensions of discrete topological complexity relate with each other. Moreover, we find a lower bound of $n-$discrete topological complexity which is given by the n-th usual topological complexity of the geometric realisation of that complex. Furthermore, we give an example for the strict case of that lower bound.

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Hilal Alabay, Ayse Borat, Esra Cihangirli, Esma Dirican Erdal. 2023-10-02. Higher Analogues of Discrete Topological Complexity. https://arxiv.org/abs/2310.01333

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