TL;DR
This paper extends Jones' planar calculus to bimodules with infinite index, generalizing key results on rotations and extremality without relying on Jones' basic construction.
Contribution
It introduces a planar calculus framework for infinite index subfactors, broadening the scope of bimodule analysis beyond finite index cases.
Findings
Generalized Jones' planar calculus to infinite index bimodules
Extended Burns' results on rotations and extremality
Achieved these results without Jones' basic construction
Abstract
We develop an analog of Jones' planar calculus for II_1-factor bimodules with arbitrary left and right von Neumann dimension. We generalize to bimodules Burns' results on rotations and extremality for infinite index subfactors. These results are obtained without Jones' basic construction and the resulting Jones projections.
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