Evasion paths by homotopy limits
Algebraic Topology
2022-11-14 v1
Abstract
The evasion paths problem asks when a dynamically changing space can be navigated: imagine guards are patrolling a region, for instance, and we need to stay outside their view. We use the Bousfield-Kan spectral sequence for homotopy inverse limits as a proxy for calculating the homotopy groups of the space of evasion paths. This gives a complete calculation of the number of paths (up to homotopy) for spaces we call ``0-sectional." We give a characterization such spaces, and conclude the paper by reframing the calculations in terms of the covered region.
Keywords
Cite
@article{arxiv.2211.05856,
title = {Evasion paths by homotopy limits},
author = {Gunnar Carlsson and Benjamin Filippenko and Wyatt Mackey},
journal= {arXiv preprint arXiv:2211.05856},
year = {2022}
}
Comments
arXiv admin note: text overlap with arXiv:2006.12023