  The paper suggests new topological lower bounds for the number of zeros of
closed 1-forms within a given cohomology class. The main new technical tool is
the deformation complex, which allows to pass to a singular limit and reduce
the original problem with a closed 1-form to a traditional problem with a Morse
function. We show by examples that the suggested approach may provide stronger
estimates than the Novikov inequalities. The technique of the paper also
applies to study topology of the set of zeros of closed 1-forms under Bott
non-degeneracy assumptions.
