  Mohar recently adapted the classical game of Cops and Robber from graphs to
metric spaces, thereby unifying previously studied pursuit-evasion games. He
conjectured that finitely many cops can win on any compact geodesic metric
space, and that their number can be upper-bounded in terms of the ranks of the
homology groups when the space is a simplicial pseudo-manifold. We disprove
these conjectures by constructing a metric on $\mathbb{S}^3$ with infinite cop
number. More problems are raised than settled.
