Length minimizing paths in the Hamiltonian diffeomorphism group

DOI10.4310/JSG.2008.V6.N2.A3zbMATH Open1151.53072arXivmath/0703738OpenAlexW2050120732MaRDI QIDQ953998

Peter Spaeth

Publication date: 7 November 2008

Published in: The Journal of Symplectic Geometry (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/math/0703738

zbMATH Keywords

symplectic manifoldFloer theoryLagrangian intersections

Mathematics Subject Classification ID

Global theory of symplectic and contact manifolds (53D35) Symplectic aspects of Floer homology and cohomology (53D40) Group structures and generalizations on infinite-dimensional manifolds (58B25)

Related Items (3)

Action minimizing properties and distances on the group of Hamiltonian diffeomorphisms ⋮ Length minimizing paths in the hyperbolic plane: proof via paired subcalibrations ⋮ Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group

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