## Algebraic & Geometric Topology

### On symplectic uniruling of Hamiltonian fibrations

Clément Hyvrier

#### Abstract

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

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

Dates
Revised: 17 February 2012
Accepted: 28 February 2012
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513715384

Digital Object Identifier
doi:10.2140/agt.2012.12.1145

Mathematical Reviews number (MathSciNet)
MR2928908

Zentralblatt MATH identifier
1250.53079

#### Citation

Hyvrier, Clément. On symplectic uniruling of Hamiltonian fibrations. Algebr. Geom. Topol. 12 (2012), no. 2, 1145--1163. doi:10.2140/agt.2012.12.1145. https://projecteuclid.org/euclid.agt/1513715384

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