Hofer’s diameter and Lagrangian intersections

@inproceedings{Polterovich1998HofersDA,
  title={Hofer’s diameter and Lagrangian intersections},
  author={Leonid Polterovich},
  year={1998}
}
  • 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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A capacity for closed symplectically aspherical manifolds

M. Schwarz
1997

Hamiltonian loops and Arnold’s

L. Polterovich
principle, Amer. Math. Soc. Transl. (2) • 1997

Relative Floer and quantum cohomology and the symplectic topology of Lagrangian submanifolds, in Contact and Symplectic Geometry, C.B

Y.-G. Oh
1996

Floer homology of Lagrangian intersections and pseudo-holomorphic discs I,II

Y.-G. Oh
Comm. Pure Appl. Math • 1993

Symplectic displacement energy for Lagrangian submanifolds

L. Polterovich
Ergodic Th. and Dynam. Syst • 1993

On the topological properties of symplectic maps

H. Hofer
Proc. Roy. Soc. Edinburgh Sect A • 1990

Cohomology of symplectomorphism groups and critical values of Hamiltonians

A. Weinstein
Math. Z • 1989

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