A note on Morse theory of harmonic 1-forms
type: Item
instance of: scholarly article
title: A note on Morse theory of harmonic 1-forms
zbMATH Open document ID: 0959.58014
DOI: 10.1016/S0040-9383(98)00018-4
author: Ko Honda
published in: Topology
publication date: 2001-04-26T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 57R45
zbMATH DE Number: 1307819
zbMATH Keywords: Morse theory
zbMATH Keywords: harmonic 1-forms
reviewed by: Dorin Andrica
MaRDI profile type: Publication
full work available at URL: s0040-9383(98)00018-4
OpenAlex ID: W2048169087
description: scientific article; zbMATH DE number 1307819