A quantum occupied multiplet that factors locally over a sphere factors globally if and only if its second Chern number is divisible by the gcd of the two subsystem dimensions.
Theories of bundles with additional homotopy conditions
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abstract
In the present paper we study bundles equipped with extra homotopy conditions, in particular so-called simplicial $n$-bundles. It is shown that (under some condition) the classifying space of 1-bundles is the double coset space of some finite dimensional Lie group. We also establish some relation between our bundles and C*-algebras.
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Entangling Topological Invariants
A quantum occupied multiplet that factors locally over a sphere factors globally if and only if its second Chern number is divisible by the gcd of the two subsystem dimensions.