Algebraic & Geometric Topology

On symplectic uniruling of Hamiltonian fibrations

Clément Hyvrier

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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].

Article information

Algebr. Geom. Topol., Volume 12, Number 2 (2012), 1145-1163.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35] 57R17: Symplectic and contact topology
Secondary: 55R10: Fiber bundles

Hamiltonian fibration Gromov–Witten invariant symplectic uniruledness Weinstein Conjecture


Hyvrier, Clément. On symplectic uniruling of Hamiltonian fibrations. Algebr. Geom. Topol. 12 (2012), no. 2, 1145--1163. doi:10.2140/agt.2012.12.1145.

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