Evasion paths by homotopy limits

2022/11/10 by Gunnar Carlsson, Benjamin Filippenko, Carlsson, Gunnar +3
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Topology (math.AT) #FOS: Mathematics #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2211.05856

openalex publication_date 2022/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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