Higher-order cyclic homology

In connection with his non-commutative geometry, Connes introduced cyclic homology. If the input is nonetheless commutative (in an appropriately generalised sense), then many exciting things occur. Among other things, there is a conjecture that one climbs the chromatic tower: "the prime factorisation of the sphere spectrum".

The questions that will be addressed in this project will be linked to a project I have with Brun (Bergen), Carlsson and Douglas (Stanford). Alexander Lundervold wrote a thesis on this topic in the spring of 2007.

Among other things, it may be necessary to study the purely algebraic structure that emerges from the higher-order deRham-Witt complex.