On symplectic uniruling of Hamiltonian fibrations

Hyvrier, Clément

doi:10.2140/agt.2012.12.1145

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On symplectic uniruling of Hamiltonian fibrations

Clément Hyvrier

Algebraic & Geometric Topology 12 (2012) 1145–1163

DOI: 10.2140/agt.2012.12.1145

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

Volume 12, issue 2 (2012)