The spectral localizer for even index pairings

Understand

Even index pairings are integer-valued homotopy invariants combining an even Fredholm module with a $K_0$-class specified by a projection.

• Numerous classical examples are known from differential and non-commutative geometry and physics.
• Here it is shown how to construct a finite dimensional selfadjoint and invertible matrix, called the spectral localizer, such that half its signature is equal to the even index pairing.
• This makes the invariant numerically accessible.