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Cops chasing a robber on hyperbolic spaces

Published on:

8 February 2024

Primary Category:

Combinatorics

Paper Authors:

Vesna Iršič,

Bojan Mohar,

Alexandra Wesolek

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Key Details

Studies Cops and Robbers game on hyperbolic surfaces and manifolds

Shows two cops suffice to capture a robber on these spaces

Result is independent of topological genus or complexity

Generalizes ideas from metric graphs and spaces to constant curvature

Provides new proof techniques based on covering spaces

AI generated summary

Cops chasing a robber on hyperbolic spaces

This paper studies a pursuit-evasion game called Cops and Robbers played on hyperbolic surfaces and manifolds. It shows that only two cops are needed to get arbitrarily close to the robber on these spaces, regardless of topological complexity. The paper generalizes techniques from graphs and geodesic metric spaces to these hyperbolic settings.

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