What is the definition of topological when talking about topological phases of matter? Why do people think that the fractional quantum hall effect is topological? I think it means that the ground state degeneracy depends on the topology of the material, whether it is a doughnut or not, and that you cannot measure which ground state the material is in with a local measurement. Is that correct?
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See discussions in http://physics.stackexchange.com/questions/70728/reconciling-topological-insulators-and-topological-order – Xiao-Gang Wen Sep 18 '14 at 14:26