Weights on bimodules (1011.1808v1)

Abstract: The concept of a {\em weight} on a planar algebra was introduced in \cite{DGG}. In this article we give an alternate characterization of weights on a planar algebra in terms of weight functions' on the vertices of the principal graphs. Using this characterization we show that the property of bifinite bimodules of having atrivial perturbation class' is closed under Connes fusion. We give a direct and constructive method of perturbing a bifinite bimodule by a positive weight in such a way that the bimodule planar algebra of the perturbed bimodule is isomorphic to the perturbation of the one associated to the initial bimodule by the given weight.