Volume 12, issue 2 (2012)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
On symplectic uniruling of Hamiltonian fibrations

Clément Hyvrier

Algebraic & Geometric Topology 12 (2012) 1145–1163
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].

Keywords
Hamiltonian fibration, Gromov–Witten invariant, symplectic uniruledness, Weinstein Conjecture
Mathematical Subject Classification 2010
Primary: 53D45, 57R17
Secondary: 55R10
References
Publication
Received: 6 April 2011
Revised: 17 February 2012
Accepted: 28 February 2012
Published: 22 May 2012
Authors
Clément Hyvrier
Mathematics Department
Uppsala Universitet
Box 480
SE-75106 Uppsala
Sweden