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.
Vaughan F. R. Jones. "Quadratic tangles in planar algebras." Duke Math. J. 161 (12) 2257 - 2295, 15 September 2012. https://doi.org/10.1215/00127094-1723608