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Crystallographic Torus Bundles: Obstructions, Elastic Sectors, and Global Acoustic Modes
We formulate the global translational order parameter of a crystal with a fixed finite orientational background as a section of an affine torus bundle induced by the crystallographic extension $1\toΠ\toΓ\to P\to1$. For a principal $P$-bundle $Q$, the configuration bundle is $Y_Π=Q\times_P T_Π$. We i
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