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Circle-invariant fat bundles and symplectic Fano 6-manifolds

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

In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, Vol. 91, No. 3, 2015, p. 709-730.

Research output: Contribution to journalArticle

Harvard

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

APA

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

Vancouver

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

Author

Fine, Joel ; Panov, Dmitri. / Circle-invariant fat bundles and symplectic Fano 6-manifolds. In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES. 2015 ; Vol. 91, No. 3. pp. 709-730.

Bibtex Download

@article{2061d609d7d64e74a22fbb4c02c9c52e,
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",
journal = "JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES",
issn = "0024-6107",
publisher = "Oxford University Press",
number = "3",

}

RIS (suitable for import to EndNote) Download

TY - JOUR

T1 - Circle-invariant fat bundles and symplectic Fano 6-manifolds

AU - Fine, Joel

AU - Panov, Dmitri

PY - 2015

Y1 - 2015

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.

UR - http://www.scopus.com/inward/record.url?scp=84941884527&partnerID=8YFLogxK

U2 - 10.1112/jlms/jdv011

DO - 10.1112/jlms/jdv011

M3 - Article

AN - SCOPUS:84941884527

VL - 91

SP - 709

EP - 730

JO - JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES

JF - JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES

SN - 0024-6107

IS - 3

ER -

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