  The topological analysis of chaos based on a knot-theoretic characterization
of unstable periodic orbits has proved a powerful method, however knot theory
can only be applied to three-dimensional systems. Still, the core principles
upon which this approach is built, determinism and continuity, apply in any
dimension. We propose an alternative framework in which these principles are
enforced on triangulated surfaces rather than curves and show that in dimension
three our approach numerically predicts the correct topological entropies for
periodic orbits of the horseshoe map.
