Electronic Research Announcements in Mathematical Sciences (ERA-MS)

Unboundedness of the Lagrangian Hofer distance in the Euclidean ball

Pages: 1 - 7, Volume 21, 2014      doi:10.3934/era.2014.21.1

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Sobhan Seyfaddini - Département de Mathématiques et Applications de l'École Normale Supérieure, 45 rue d'Ulm, F 75230 Paris cedex 05, France (email)

Abstract: Let $\mathcal{L}$ denote the space of Lagrangians Hamiltonian isotopic to the standard Lagrangian in the unit ball in $\mathbb{R}^{2n}$. We prove that the Lagrangian Hofer distance on $\mathcal{L}$ is unbounded.

Keywords:  Symplectic manifolds, Hofer's distance, quasimorphisms.
Mathematics Subject Classification:  Primary: 53D40; Secondary 37J05.

Received: October 2013;      Revised: November 2013;      Available Online: January 2014.