r^sharp discriminates between regimes where H-flux survives T-duality or converts to geometric flux on product manifolds with product metrics.
Agricola,The Srn´ ı lectures on non-integrable geometries with torsion, Arch
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The $r^\sharp$ invariant as a discriminant for the survival of the H-flux under T-duality on product manifolds
r^sharp discriminates between regimes where H-flux survives T-duality or converts to geometric flux on product manifolds with product metrics.