arXiv subjects

Clement Hyvrier

Publications and source records attributed to Clement Hyvrier.

2 recordsLinked to original sources

arXiv2013

Lagrangian Circle Actions

We consider paths of Hamiltonian diffeomorphism preserving a given compact monotone Lagrangian in a symplectic manifold that extend to an $S^1$--Hamiltonian action. We compute the leading term of the associated Lagrangian Seidel element. We show that such paths minimize the Lagrangian Hofer length. Finally we apply these computations to Lagrangian uniruledness and to give a nice presentation of the Quantum cohomology of real lagrangians in Fano symplectic toric manifolds.

math.SG↗

arXiv2011

The Weinstein Conjecture for Hamiltonian Fibrations

In this note we extend to non trivial Hamiltonian fibrations over symplectically uniruled manifolds a result of Lu's, \cite{Lu}, 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, under certain technical conditions. The proof is based on the product formula for Gromov-Witten invariants ($GW$-invariant) of Hamiltonian fibrations derived in \cite{H}.

math.SG↗