2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77871We study the behavior of the spectrum of the Dirac operator on collapsing S^1-bundles. Convergent eigenvalues will exist if and only if the spin structure is projectable.11 pages, Latex2e, to appear in "Se'minaire de The'orie Spectrale et Ge'ome'trie" Institut Fourier, Grenoble, vol. 16, 1997-98Differential GeometrySpectral Theory58G25, 58G30, 53C25text