Hofer’s norm of Hamiltonian commutators

Jeudi 14 avril 2016 14:00-15:00 - Michael Khanevsky - Université Libre de Bruxelles

Résumé : In 1990 H. Hofer introduced a remarkable conjugation invariant norm on the group of Hamiltonian diffeomorphisms of a manifold $M$. This norm can be seen as the mechanical « energy » needed to perform a deformation. It also induces a metric which allows to approach Hamiltonian dynamics using geometric tools. Chekanov proved that the energy needed to displace a Lagrangian $L$ away from itself is bounded from below by the minimal area of holomorphic spheres and disks in $(M ;L)$. We discuss a similar bound by Usher for the energy needed to separate a pair of Lagrangian submanifolds in $M$. An application of this estimate shows that certain manifolds admit Hamiltonian commutators with large Hofer’s norm. This implies that Hofer’s norm is not equivalent to the commutator norm.

Lieu : Bâtiment 425, salle 121-123

Notes de dernières minutes : Café culturel assuré à 13h par Rémi Leclercq.

Hofer’s norm of Hamiltonian commutators  Version PDF