TL;DR
This paper introduces a method for projecting quadratic tangles in planar algebras onto simpler linear and constant tangles, providing insights into subfactor structures.
Contribution
It presents a novel projection technique for quadratic tangles in planar algebras, with implications for understanding principal graphs and annular structures.
Findings
Projection of quadratic tangles onto linear and constant tangles
Corollaries on principal graphs of subfactors
Results on annular structure of subfactors
Abstract
In planar algebras, we show how to project certain simple "quadratic" tangles onto the linear space spanned by "linear" and "constant" tangles. We obtain some corollaries about the principal graphs and annular structure of subfactors.
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