• Citer

Circle-invariant fat bundles and symplectic Fano 6-manifolds

par Fine, Joel ;Panov, Dmitri
Référence Journal of the London Mathematical Society, 91, 3, page (709-730)
Publication Publié, 2015

Article révisé par les pairs

• Accès en ligne
• Détails
• Contenu
• Statistiques

Résumé :

We prove that a compact 4-manifold which supports a circle-invariant fat SO(3)-bundle is diffeomorphic to either S4 or ℂℙ2. The proof involves studying the resulting Hamiltonian circle action on an associated symplectic 6-manifold. Applying our result to the twistor bundle of Riemannian 4-manifolds shows that S4 and ℂℙ2 are the only 4-manifolds admitting circleinvariant metrics solving a certain curvature inequality. This can be seen as an analogue of Hsiang-Kleiner's theorem that only S4 and ℂℙ2 admit circle-invariant metrics of positive sectional curvature.