Journal of Symplectic Geometry

Volume 6 (2008)

Number 2

Length minimizing paths in the Hamiltonian diffeomorphism group

Pages: 159 – 187

DOI: http://dx.doi.org/10.4310/JSG.2008.v6.n2.a3

Author

Peter W. Spaeth

Abstract

On any closed symplectic manifold, we construct a path-connected neighborhood of the identity in the Hamiltonian diffeomorphism group with the property that each Hamiltonian diffeomorphism in this neighborhood admits a Hofer and spectral length minimizing path to the identity. This neighborhood is open in the $C^1$-topology. The construction utilizes a continuation argument and chain level result in the Floer theory of Lagrangian intersections.

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