In particular, he produced examples showing that the converse of the Hitchin–Thorpe inequality does not hold: there exist infinitely many four-dimensional compact smooth simply connected manifolds that obey the inequality but do not admit Einstein metrics.
Claude Monet | Claude Debussy | Claude Lorrain | Claude François | Jean-Claude Van Damme | Claude Lévi-Strauss | Claude Royet-Journoud | Claude Chabrol | Jean-Claude Carrière | Claude Vivier | Claude Shannon | Claude Berri | Jean-Claude Colin | Claude Rains | Claude Bowes-Lyon, 13th Earl of Strathmore and Kinghorne | Christo and Jeanne-Claude | Jean-Claude Gérard | Claude Lelouch | Claude Jade | Claude Garamond | Claude Bolling | Claude Auchinleck | Jean-Claude Duvalier | Claude Thornhill | Claude Simon | Claude Nicollier | Claude Mollet | Claude Lecouteux | Claude Joseph Vernet | Claude Dubois |