2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67201An inclusion of II$_1$ factors $N \subset M$ with finite Jones index gives rise to a powerful set of invariants that can be approached successfully in a number of different ways. We describe Jones' pictorial description of the standard invariant of a subfactor as a so-called planar algebra and show how this point of view leads to new structure results for subfactors.Operator Algebras46L37, 46L60, 82B20, 81T05text