On the connectivity properties of the solution set of parametrized families of compact vector fields
An extension to n-parameter families of compact vector fields of the well-known Leray-Schauder continuation principle is obtained. Using Čech cohomology, it is proved that (under the usual assumptions) the zero-set of the family contains a closed connected subset of dimension at least n whose projection covers all of the parameters space. See also [\textit{P. M. Fitzpatrick} and the authors Math. Ann. 263, 61-73 (1983; Zbl 0519.58024)].
n-parameter families of compact vector fields
scientific article; zbMATH DE number 3895732
scientific article