  We propose an experiment to observe the topological phases associated with
cyclic evolutions, generated by local SU(2) operations, on three-qubit
entangled states prepared on different degrees of freedom of entangled photon
pairs. The topological phases reveal the nontrivial topological structure of
the local SU(2) orbits. We describe how to prepare states showing different
topological phases, and discuss their relation to entanglement. In particular,
the presence of a $\pi/2$ phase shift is a signature of genuine tripartite
entanglement in the sense that it does not exist for two-qubit systems.
