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In this talk, I will present recent results in the entanglement
entropy of gapped quantum phases of matter. In particular, I will
focus on the following two results:
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**The topological entanglement entropy for some of the known topological states in three and higher dimensions has an interesting dependence on the Betti numbers of the boundary manifold defined by the entanglement cut.****In contrast to the familiar result in two dimensions, a size independent constant contribution to the entanglement entropy can appear for non-topological phases in any odd spatial dimension.**

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