An odd index theorem for higher odd Chern characters of crossed product algebras is proved. It generalizes the Noether-Gohberg-Krein index theorem. Furthermore, a local formula for the associated cyclic cocycle is provided. When applied to the non-commutative Brillouin zone, this allows to define topological invariants for condensed matter phases from the chiral unitary (or AIII-symmetry) class in the presence of strong disorder and magnetic fields whenever the Fermi level lies in region of Anderson localization.
- Pub Date:
- February 2014
- Mathematical Physics;
- Condensed Matter - Disordered Systems and Neural Networks;
- Mathematics - Operator Algebras
- Final Version to appear in J. Funct. Anal., several corrections and improvements based on referee reports