Circle-invariant fat bundles and symplectic Fano 6-manifolds

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

SN - 0024-6107

VL - 91

SP - 709

EP - 730

JO - JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES

JF - JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES

IS - 3

ER -