Open Access
2012 On symplectic uniruling of Hamiltonian fibrations
Clément Hyvrier
Algebr. Geom. Topol. 12(2): 1145-1163 (2012). DOI: 10.2140/agt.2012.12.1145


Under certain conditions of technical order, we show that closed connected Hamiltonian fibrations over symplectically uniruled manifolds are also symplectically uniruled. As a consequence, we partially extend to nontrivial Hamiltonian fibrations a result of Lu [Math. Res. Lett. 7 (2000) 383–387], stating that any trivial symplectic product of two closed symplectic manifolds with one of them being symplectically uniruled verifies the Weinstein Conjecture for closed separating hypersurfaces of contact type. The proof of our result is based on the product formula for Gromov–Witten invariants of Hamiltonian fibrations derived by the author in [arXiv 0904.1492].


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Clément Hyvrier. "On symplectic uniruling of Hamiltonian fibrations." Algebr. Geom. Topol. 12 (2) 1145 - 1163, 2012.


Received: 6 April 2011; Revised: 17 February 2012; Accepted: 28 February 2012; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1250.53079
MathSciNet: MR2928908
Digital Object Identifier: 10.2140/agt.2012.12.1145

Primary: 53D45 , 57R17
Secondary: 55R10

Keywords: Gromov–Witten invariant , Hamiltonian fibration , symplectic uniruledness , Weinstein Conjecture

Rights: Copyright © 2012 Mathematical Sciences Publishers

Vol.12 • No. 2 • 2012
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