Mathematics – Symplectic Geometry
Scientific paper
2001-04-25
Asian J. Math. 6 (2002) 579-624
Mathematics
Symplectic Geometry
Section 6 concerning adic (or adiabadic) limit of Floer's moduli space is removed and so sections and proofs are reorganized
Scientific paper
In this paper we first apply the chain level Floer theory to the study of Hofer's geometry of Hamiltonian diffeomorphism group in the cases without quantum contribution: we prove that any quasi-autonomous Hamiltonian path on weakly exact symplectic manifolds or any autonomous Hamiltonian path on arbitrary symplectic manifolds is length minimizing in its homotopy class with fixed ends, as long as it has a fixed maximum and a fixed minimum which are not over-twisted and all of its contractible periodic orbits of period less than one are sufficiently $C^1$-small. Next we give a construction of new invariant norm of Viterbo's type on the Hamiltonian diffeomorphism group of arbitrary compact symplectic manifolds.
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