Research output: Contribution to journal › Article

**Circle-invariant fat bundles and symplectic Fano 6-manifolds.** / Fine, Joel; Panov, Dmitri.

Research output: Contribution to journal › Article

Fine, J & Panov, D 2015, 'Circle-invariant fat bundles and symplectic Fano 6-manifolds', *JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES*, vol. 91, no. 3, pp. 709-730. https://doi.org/10.1112/jlms/jdv011

Fine, J., & Panov, D. (2015). Circle-invariant fat bundles and symplectic Fano 6-manifolds. *JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES*, *91*(3), 709-730. https://doi.org/10.1112/jlms/jdv011

Fine J, Panov D. Circle-invariant fat bundles and symplectic Fano 6-manifolds. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES. 2015;91(3):709-730. https://doi.org/10.1112/jlms/jdv011

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title = "Circle-invariant fat bundles and symplectic Fano 6-manifolds",

abstract = "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.",

author = "Joel Fine and Dmitri Panov",

year = "2015",

doi = "10.1112/jlms/jdv011",

language = "English",

volume = "91",

pages = "709--730",

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AU - Fine, Joel

AU - Panov, Dmitri

PY - 2015

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N2 - 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.

AB - 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.

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U2 - 10.1112/jlms/jdv011

DO - 10.1112/jlms/jdv011

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JO - JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES

JF - JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES

SN - 0024-6107

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