Proper topological complexity
Algebraic Topology
2025-01-27 v2
Abstract
We introduce and study the proper topological complexity of a given configuration space, a version of the classical invariant for which we require that the algorithm controlling the motion is able to avoid any possible choice of ``unsafe'' area. To make it a homotopy functorial invariant we characterize it as a particular instance of the exterior sectional category of an exterior map, an invariant of the exterior homotopy category which is also deeply analyzed.
Cite
@article{arxiv.2407.16679,
title = {Proper topological complexity},
author = {Jose M. Garcia-Calcines and Aniceto Murillo},
journal= {arXiv preprint arXiv:2407.16679},
year = {2025}
}
Comments
28 pages, 1 figure