Cops and Robber on Hyperbolic Manifolds
8 February 2024
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
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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