A note on Morse theory of harmonic 1-forms
Using the characterization of intrinsically harmonic 1-forms given by \textit{E. Calabi} [in ``Global Analysis'', Papers in Honor of K. Kodeira, 101-117 (1969; Zbl 0194.24701)] the author proves the following theorem: Let \(\omega_0\) be a generic 1-form with no zeros of index 0 or \(n\). Then there exists a family of generic 1-forms \(\omega_t\), \(t\in[0,1]\), with \([\omega_t]\in H^1(M;\mathbb{R})\) fixed, such that \(\omega_1\) is intrinsically harmonic and each \(\omega_t\) has the same number of zeros of each index. Here, a closed 1-form \(\omega\) is generic if, as a section of the cotangent bundle \(T^*M\), it is transverse to the zero section.
scientific article; zbMATH DE number 1307819