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We discuss entanglement entropy of gapped ground states in different dimensions, obtained on partitioning space into two regions.
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Heuristically, the Betti number b k b_{k} measures the dimension of k k -dimensional closed surfaces within a manifold that are not boundaries of a k + 1 k+1 -dimensional surface. See, e.g., Chapter 3 of Ref. [ 12 ] for an introduction
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The same symmetry is responsible for relating corner contributions to the entanglement entropy with angles θ \theta and 2 π − θ 2\pi-\theta [ 5 , 21 ]
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