Classification of approximately inner automorphisms of subfactors (Q1364561)

For classification of approximately inner automorphisms of subfactors, we introduce a new invariant, a higher obstruction. From an algebraic viewpoint, this can be regarded as a generalization of the Connes obstruction, and from an analytic viewpoint, this can be regarded as a generalization of the Jones invariant \(\kappa\). We have two classification theorems for approximately inner automorphisms of strongly amenable subfactors with known invariants and this new one. In particular, our theorems give a complete classification of automorphisms, up to outer conjugacy, of AFD subfactors of type \(\text{II}_1\) with index less than four except for one special case for \(A_{4n-1}\) and \(E_6\).