THE SCHOCHET SPECTRAL SEQUENCE FOR NONCOMMUTATIVE CW-COMPLEXES

Noncommutative CW-Complexes can be constructed by dualizing the classical construction and allowing the C*-algebras to be noncommutative. Then the topological invariants, such as K-groups, can be determined up to the ambiguity of group extensions involving torsion by chasing six-term exact sequences in K-theory. A way to organize these exact sequences is provided by spectral sequences. In this talk, we will study the Schochet Spectral Sequence for filtered C*-algebras, where the filtration arises from the kernels of projections onto the C*-algebras of lower skeletons. While the first differential can be related nicely to its classical analog, it is not yet clear to us how to do it for higher differentials. This is work in progress in collaboration with Arley Sierra Acosta.