On properties of effective topological complexity and effective Lusternik-Schnirelmann category
Abstract
The notion of effective topological complexity, introduced by B{\l}aszczyk and Kaluba, deals with using group actions in the configuration space in order to reduce the complexity of the motion planning algorithm. In this article we focus on studying several properties of such notion of topological complexity. We introduce a notion of effective LS-category which mimics the behaviour the usual LS-cat has in the non-effective setting. We use it to investigate the relationship between these effective invariants and the orbit map with respect of the group action, and we give numerous examples. Additionally, we investigate non-vanishing criteria based on a cohomological dimension bound of the saturated diagonal.
Keywords
Cite
@article{arxiv.2402.18524,
title = {On properties of effective topological complexity and effective Lusternik-Schnirelmann category},
author = {Zbigniew Błaszczyk and Arturo Espinosa Baro and Antonio Viruel},
journal= {arXiv preprint arXiv:2402.18524},
year = {2024}
}
Comments
31 pages, 1 figure. Several improvements and corrections of typos, some additional results added. Preliminary version, comments are most welcomed!