In this paper we illustrate usage of chain level Floer theory in the study of Hofer’s geometry of Hamiltonian diffeomorphism group. Among several examples, we give a new proof of Lalonde-McDuff’s… (More)

In this paper, we apply spectral invariants, constructed in [Oh5,8], to the study of Hamiltonian diffeomorphisms of closed symplectic manifolds (M, ω). Using spectral invariants, we first construct… (More)

In this paper, we develop a mini-max theory of the action functional over the semi-infinite cycles via the chain level Floer homology theory and construct spectral invariants of Hamiltonian… (More)

In this paper, we first develop a mini-max theory of the action functional over the semi-infinite cycles via the chain level Floer homology theory and construct spectral invariants of Hamiltonian… (More)

In this paper we provide a criterion for the quasi-autonomous Hamiltonian path (“Hofer’s geodesic”) on arbitrary closed symplectic manifolds (M, ω) to be length minimizing in its homotopy class in… (More)

In this paper, we give a new simple proof of Chekanov’s positivity theorem of the disjunction energy of compact Lagrangian submanifolds in tame symplectic manifolds. As a consequence, it also gives… (More)

In this paper, we apply the spectral invariants, constructed in [Oh5,8], to the study of Hamiltonian diffeomorphisms of closed symplectic manifolds (M, ω). Using the spectral invariants, we first… (More)

The author previously defined the spectral invariants, denoted by ρ(H; a), of a Hamiltonian function H as the mini-max value of the action functional AH over the Novikov Floer cycles in the Floer… (More)

In this paper, we develop a mini-max theory of the action functional over the semi-infinite cycles via the chain level Floer homology theory and construct spectral invariants of Hamiltonian… (More)