1,235 research outputs found
Floer cohomology of Lagrangian intersections and pseudo-holomorphic disks. I.Addendum
No full textThis is an addendum to the author's earlier paper ''Floer Cohomology of Lagrangian Intersection and Pseudo-Holomorphic Discs, I,'' Comm. Pure Appl. Math. 46, 1993, pp. 949-993. The main result of this addendum extends the definition of the Fleer cohomology of Lagrangian intersection to the case where the minimal Maslov number is equal to 2. (C) 1996 John Wiley & Sons, Inc.X1145sciescopu
Spectral invariants and the length minimizing property of Hamiltonian paths
No full textIn this paper we provide a criterion for the quasi-autonomous Hamiltonian path ("Hofer's geodesic") on arbitrary closed symplectic manifolds (M, omega) to be length minimizing in its homotopy class in terms of the spectral invariants rho(G; 1) that the author has recently constructed. As an application, we prove that any autonomous Hamiltonian path on arbitrary closed symplectic manifolds is length minimizing in its homotopy class with fixed ends, as long as it has no contractible periodic orbits of period one and it has a maximum and a minimum that are generically under-twisted, and all of its critical points are non-degenerate in the Floer theoretic sense.X1110sci
Floer mini-max theory, the Cerf diagram, and the spectral invariants
No full textThe author previously defined the spectral invariants, denoted by rho(H; a), of a Hamiltonian function H as the mini-max value of the action functional A(H) over the Novikov Floer cycles in the Floer homology class dual to the quantum cohomology class a. The spectrality axiom of the invariant rho(H; a) states that the mini-max value is a critical value of the action functional AH. The main purpose of the present paper is to prove this axiom for nondegenerate Hamiltonian functions in irrational symplectic manifolds (M, omega). We also prove that the spectral invariant function rho(a) : H (sic) rho(H; a) can be pushed down to a continuous function defined on the universal (etale) covering space (sic)(M,omega) of the group Ham(M,omega) of Hamiltonian diffeomorphisms on general (M, omega). For a certain generic homotopy, which we call a Cerf homotopy H = {H(s)}(0 <= s <= 1) of Hamiltonians, the function rho(a) circle H : s (sic) rho(H(s); a) is piecewise smooth away from a countable subset of [0,1] for each non-zero quantum cohomology class a. The proof of this nondegenerate spectrality relies on several new ingredients in the chain level Floer theory, which have their own independent interest: a structure theorem on the Cerf bifurcation diagram of the critical values of the action functionals associated to a generic one-parameter family of Hamiltonian functions, a general structure theorem and the handle sliding lemma of Novikov Floer cycles over such a family and a family version. of new transversality statements involving the Floer chain map, and many others. We call this chain level Floer theory as a whole the Floer mini-max theory.X118sciescopuskc
Contrasting enrichments in high- and low-temperature mantle xenoliths from Nushan, eastern China: Results of a single metasomatic event during lithospheric accretion?
No full textOsmium, lead and neodymium isotope geochemistry of Permian Emeishan continental flood basalts: Insights into the source of a large igneous province
No full textContinuous Hamiltonian dynamics and area-preserving homeomorphism group of D2
No full textThe main purpose of this paper is to propose a scheme of a proof of the nonsimpleness of the group {\rm Homeo}^\Omega(D^2,\del D^2) of area preserving homeomorphisms of the 2-disc . We first establish the existence of Alexander isotopy in the category of Hamiltonian homeomorphisms. This reduces the question of extendability of the well-known Calabi homomorphism \Cal: {\rm Diff}^\Omega(D^1,\del D^2) \to \R to a homomorphism \overline \Cal: {\rm Hameo(}D^2,\del D^2) \to \R to that of the vanishing of the basic phase function , a Floer theoretic graph selector constructed in \cite{oh:jdg}, that is associated to the graph of the topological Hamiltonian loop and its normalized Hamiltonian on that is obtained via the natural embedding . Here {\rm Hameo(}D^2,\del D^2) is the group of Hamiltonian homeomorphisms introduced by M\"uller and the author \cite{oh:hameo1}. We then provide an evidence of this vanishing conjecture by proving the conjecture for the special class of \emph{weakly graphical} topological Hamiltonian loops on via a study of the associated Hamiton-Jacobi equation.1111Ysciescopuskc
Parameters of Coseismic Reverse- and Oblique-Slip Surface Ruptures of the 2008 Wenchuan Earthquake, Eastern Tibetan Plateau.
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Integration of geology, geophysics and geochemistry: A key to understanding the North China Craton
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