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Glossary Of Symplectic Geometry
This is a glossary of properties and concepts in symplectic geometry in mathematics. The terms listed here cover the occurrences of symplectic geometry both in topology as well as in algebraic geometry (over the complex numbers for definiteness). The glossary also includes notions from Hamiltonian geometry, Poisson geometry and geometric quantization. In addition, this glossary also includes some concepts (e.g., virtual fundamental class) in intersection theory that appear in symplectic geometry as they do not naturally fit into other lists such as the glossary of algebraic geometry. A C D E F H I K L M N P Q S T V Notes References * *Kontsevich, M. Enumeration of rational curves via torus actions. Progr. Math. 129, Birkhauser, Boston, 1995. *Meinrenken'lecture notes on symplectic geometry* * External ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symplectic Geometry
Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed differential form, closed, nondegenerate form, nondegenerate differential form, 2-form. Symplectic geometry has its origins in the Hamiltonian mechanics, Hamiltonian formulation of classical mechanics where the phase space of certain classical systems takes on the structure of a symplectic manifold. The term "symplectic", introduced by Weyl, is a calque of "complex"; previously, the "symplectic group" had been called the "line complex group". "Complex" comes from the Latin ''com-plexus'', meaning "braided together" (co- + plexus), while symplectic comes from the corresponding Greek ''sym-plektikos'' (συμπλεκτικός); in both cases the stem comes from the Indo-European root wiktionary:Reconstruction:Proto-Indo-European/pleḱ-, *pleḱ- The name reflects the deep connections between complex and sym ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Novikov Ring
In mathematics, given an additive subgroup \Gamma \subset \R, the Novikov ring \operatorname(\Gamma) of \Gamma is the subring of \Z Gamma.html" ;"title="![\Gamma">![\Gamma!/math>Here, \Z Gamma.html" ;"title="![\Gamma">![\Gamma!/math> is the ring consisting of the formal sums \sum_ n_\gamma t^\gamma, n_\gamma integers and ''t'' a formal variable, such that the multiplication is an extension of a multiplication in the integral group ring \Z[\Gamma]. consisting of formal sums \sum n_ t^ such that \gamma_1 > \gamma_2 > \cdots and \gamma_i \to -\infty. The notion was introduced by Sergei Novikov in the papers that initiated the generalization of Morse theory using a closed one-form instead of a function. The notion is used in quantum cohomology, among the others. The Novikov ring \operatorname(\Gamma) is a principal ideal domain. Let ''S'' be the subset of \Z[\Gamma] consisting of those with leading term 1. Since the elements of ''S'' are unit elements of \operatorname(\Gamma), the Loca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
