Abstract
Consider an inclusion of diffuse von Neumann algebras [Formula: see text]. We say that [Formula: see text] has the absorbing amenability property (AAP) if for any diffuse subalgebra [Formula: see text] and any amenable intermediate algebra [Formula: see text] we have that [Formula: see text] is contained in [Formula: see text] We prove that the cup subalgebra associated to any subfactor planar algebra has the AAP.
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