Counting zeros of closed 1-forms (Q2735113)

This paper provides 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 the author to pass to a singular limit and reduce the original problem with closed 1-forms to a traditional problem with a Morse function. The authors show by examples that the new approach may provide stronger estimates than the Novikov inequalities. The results can be applied to study a set of zeros of a closed 1-form under Bott nondegeneracy assumptions.NEWLINENEWLINEFor the entire collection see [Zbl 0961.00011].