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arXiv · 1407.0840

Circle-invariant fat bundles and symplectic Fano 6-manifolds

Joel Fine·Dmitri Panov
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Abstract

We prove that a compact 4-manifold which supports a circle-invariant fat SO(3)-bundle is diffeomorphic to either S^4 or CP^2-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 S^4 and CP^2-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 S^4 and CP^2 admit circle-invariant metrics of positive sectional curvature.

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Joel Fine, Dmitri Panov. 2014-07-03. Circle-invariant fat bundles and symplectic Fano 6-manifolds. https://doi.org/10.1112/jlms%2Fjdv011

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