The cohomology bundle is a flat complex vector bundle on . Hence, there is a natural flat connection on the sheaf of holomorphic sections in with covariant derivative . It induces a differential operator on where denotes the inclusion.
Let , , be the universal covering of and the canonical Milnor fibre. Then the natural maps , , are homotopy equivalences. Hence, can be considered as the space of global flat multivalued sections in and as a trivial complex vector bundle on .