Describing the geometry of differentiable manifolds equipped with a closed, nondegenerate 2-form

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  • Symplectic — Sym*plec tic, a. [Gr. ? plaiting together, fr. ? to plait together.] (Anat.) Plaiting or joining together; said of a bone next above the quadrate in the mandibular suspensorium of many fishes, which unites together the other bones of the… …   The Collaborative International Dictionary of English

  • symplectic — I. (ˈ)sim|plektik adjective Etymology: Greek symplektikos of intertwining, from symplektos (verbal of symplekein to plait together, intertwine, from syn + plekein to plait) + ikos ic more at ply 1. : relating to or being an intergrowth of two… …   Useful english dictionary

  • symplectic — the small, paired, deep, endochondral bone joining the quadrate and the hyomandibular and supporting the interhyal in the hyostylic jaw (q.v.). It is cartilaginous in Acipenser and absent in Siluroidei and Anguilloidei …   Dictionary of ichthyology

  • symplectic — sym·plec·tic …   English syllables

  • Symplectic geometry — is a branch of differential topology/geometry which studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2 form. Symplectic geometry has its origins in the Hamiltonian formulation of classical… …   Wikipedia

  • Symplectic sum — In mathematics, specifically in symplectic geometry, the symplectic sum is a geometric modification on symplectic manifolds, which glues two given manifolds into a single new one. It is a symplectic version of connected summation along a… …   Wikipedia

  • Symplectic manifold — In mathematics, a symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2 form, ω, called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology.… …   Wikipedia

  • Symplectic vector space — In mathematics, a symplectic vector space is a vector space V equipped with a nondegenerate, skew symmetric, bilinear form omega; called the symplectic form. Explicitly, a symplectic form is a bilinear form omega; : V times; V rarr; R which is *… …   Wikipedia

  • Symplectic cut — In mathematics, specifically in symplectic geometry, the symplectic cut is a geometric modification on symplectic manifolds. Its effect is to decompose a given manifold into two pieces. There is an inverse operation, the symplectic sum, that… …   Wikipedia

  • Symplectic group — For finite groups with all characteristc abelian subgroups cyclic, see group of symplectic type. Group theory …   Wikipedia

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