2014/07/03 by Joel Fine, Dmitri Panov
Mathematics · #math.DG #math.SG
paper · pdf · doi:10.1112/jlms/jdv011
published as Journal of the London Mathematical Society, (2) 91 (2015), no. 3, 709--730 · 26 pages
arxiv created 2014/07/03 · arxiv updated 2017/05/17
We prove that a compact 4-manifold which supports a circle-invariant fat SO(3)-bundle is diffeomorphic to either S4 or CP2-bar. 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-bar are the only 4-manifolds admitting circle-invariant metrics solving a certain curvature inequality. This can be seen as an analogue of Hsiang-Kliener's theorem that only S4 and CP2 admit circle-invariant metrics of positive sectional curvature.