English

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

R2 v1 2026-06-28T05:38:06.498Z