  For a smooth, closed $n$-manifold $M$, we define an upper semi-continuous
integer-valued complexity function on $H^1(M;{\mathbb R})$ using Morse theory.
This measures how far an integral class is from being a fiber of a fibration.
The fact complexity minimisers are open generalises Tischler's result on the
openness of classes dual to fibrations. We then use this to define a complexity
function on 1-dimensional cohomology of a finitely presented group, which is
constant on open rays from the origin and vanishes precisely on the geometric
invariant due to Bieri, Neumann and Strebel.
