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 .