# NCG

## Seminar

### A noncommutative sheaf theory

Seminar Room 1, Newton Institute

#### Abstract

Modules with flat connection over algebras with differential structure have several properties in common with sheaf theory over topological spaces. In particular they admit long exact sequences for a cohomology theory. However sheaf theory is best described by looking at its applications, one of which is the Serre spectral sequence for a topological fibration. In the case where the cohomology of the fiber is not a trivial bundle over the base, sheaf cohomology is required to make sense of the resulting cohomology theory. I will describe a noncommutative version of the Serre spectral sequence for de Rham cohomology, which uses flat connections. This will effectively specify a definition of differential fibration in noncommutative geometry. I will then consider examples, which are quantum homogenous spaces.