  For a general quantum many-body system, we show that its ground-state
entanglement imposes a fundamental constraint on the low-energy excitations.
For two-dimensional systems, our result implies that any system that supports
anyons must have a nonvanishing topological entanglement entropy. We
demonstrate the generality of this argument by applying it to three-dimensional
quantum many-body systems, and showing that there is a pair of ground state
topological invariants that are associated to their physical boundaries. From
the pair, one can determine whether the given boundary can or cannot absorb
point-like or line-like excitations.
