Conformal Nets and KK-Theory

Strong Additivity and Conformal Nets

We show that the fixed point subnet of a strongly additive conformal net under the action of a compact group is strongly additive. Using the idea of the proof we define the notion of strong additivity for a pair of conformal nets and we show that a key result about the induction of the pair which we proved previously under the finite index assumption can be generalized to strongly additive pair...

Equivariant KK-theory and noncommutative index theory

On intermediate conformal nets

Let A be a completely rational net and A ⊂ B an extension of A with finite index. In this talk we will describe a recent general result which shows that the (maximal version of ) generalized Wall’s conjecture is true for the pair A ⊂ B. When combined with earlier results on cosets and conformal inclusions, this gives infinite families of subfactors from CFT which verify generalized Wall’s conje...

Conformal Nets and Topological Modular Forms

Project Summary: Some mathematical notions can be described in both algebraic and geometric ways. The geometric descriptions are sometimes richer and can reveal hidden symmetries. K-theory is an example of a theory that has both and algebraic and geometric description. It links algebraic topology with geometry on curved spaces, to the mutual benefit of both disciplines. We believe that the noti...

L-index theorems, KK-theory, and connections

Let M be a compact manifold. and D a Dirac type differential operator on M . Let A be a C ∗-algebra. Given a bundle W of A-modules over M (with connection), the operator D can be twisted with this bundle. One can then use a trace on A to define numerical indices of this twisted operator. We prove an explicit formula for this index. Our result does complement the Mishchenko-Fomenko index theorem...