Hofer’s diameter and Lagrangian intersections

  title={Hofer’s diameter and Lagrangian intersections},
  author={Leonid Polterovich},
  • Leonid Polterovich
  • Published 1998
The purpose of the present note is to show that the group of Hamiltonian diffeomorphisms of the 2-sphere has infinite diameter with respect to Hofer’s metric. For surfaces of higher genus this fact follows from the energy-capacity inequality in the universal cover (see Lalonde-McDuff [LM], and a recent preprint by M. Schwarz [S] which establishes infiniteness of Hofer’s diameter for arbitrary aspherical symplectic manifolds). Our approach is based on a reduction of the statement to certain… CONTINUE READING
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