• Thumbnail for Symplectic geometry
    Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds...
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  • Thumbnail for Contact geometry
    content of the Frobenius theorem. Contact geometry is in many ways an odd-dimensional counterpart of symplectic geometry, a structure on certain even-dimensional...
    20 KB (2,527 words) - 18:15, 5 June 2025
  • \omega } , called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology. Symplectic manifolds arise naturally...
    23 KB (3,674 words) - 20:57, 8 March 2025
  • properties and concepts in symplectic geometry in mathematics. The terms listed here cover the occurrences of symplectic geometry both in topology as well...
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  • Thumbnail for Differential geometry
    example, in Riemannian geometry distances and angles are specified, in symplectic geometry volumes may be computed, in conformal geometry only angles are specified...
    46 KB (5,964 words) - 21:55, 19 May 2025
  • In mathematics, a symplectic vector space is a vector space V {\displaystyle V} over a field F {\displaystyle F} (for example the real numbers R {\displaystyle...
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  • Maurice de Gosson: Symplectic Geometry and Quantum Mechanics (2006), p.7 and pp. 12–13 da Silva, A.C., Lectures on Symplectic Geometry, Springer (2001)...
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  • Thumbnail for Vladimir Arnold
    systems, algebra, catastrophe theory, topology, real algebraic geometry, symplectic geometry, differential equations, classical mechanics, differential-geometric...
    52 KB (5,072 words) - 00:13, 4 June 2025
  • Thumbnail for Symplectic group
    In mathematics, the name symplectic group can refer to two different, but closely related, collections of mathematical groups, denoted Sp(2n, F) and Sp(n)...
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  • Thumbnail for Mikhael Gromov (mathematician)
    existence of exact Lagrangian immersions and similar objects in symplectic and contact geometry. His well-known book Partial Differential Relations collects...
    48 KB (3,749 words) - 17:22, 27 May 2025
  • manifold Symplectic topology Symplectic space Symplectic manifold Symplectic structure Symplectomorphism Contact structure Contact geometry Hamiltonian...
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  • refer to: Symplectic category Symplectic Clifford algebra, see Weyl algebra Symplectic geometry Symplectic group, and corresponding symplectic Lie algebra...
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  • momentum coordinates is available in the mathematical setting of symplectic geometry. Liouville's theorem ignores the possibility of chemical reactions...
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  • A symplectic space may refer to: Symplectic manifold Symplectic vector space This disambiguation page lists articles associated with the title Symplectic...
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  • symplectic form ω {\displaystyle \omega } , but satisfies the same algebraic properties. Poisson geometry is closely related to symplectic geometry:...
    87 KB (12,665 words) - 19:20, 4 June 2025
  • is a British mathematician who deals with symplectic manifolds and their interaction with algebraic geometry, low-dimensional topology, and dynamics. He...
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  • In mathematics, specifically in symplectic geometry, the momentum map (or, by false etymology, moment map) is a tool associated with a Hamiltonian action...
    14 KB (2,215 words) - 19:34, 24 May 2025
  • mathematics, a symplectic vector field is one whose flow preserves a symplectic form. That is, if ( M , ω ) {\displaystyle (M,\omega )} is a symplectic manifold...
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  • symplectic geometry. It was first proven in 1985 by Mikhail Gromov. The theorem states that one cannot embed a ball into a cylinder via a symplectic map...
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  • Ruppeiner geometry Solid geometry Spherical geometry Symplectic geometry Synthetic geometry Systolic geometry Taxicab geometry Toric geometry Transformation...
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  • Thumbnail for Kenji Fukaya
    1959) is a Japanese mathematician known for his work in symplectic geometry and Riemannian geometry. His many fundamental contributions to mathematics include...
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  • Thumbnail for Hamiltonian mechanics
    phenomena. Hamiltonian mechanics has a close relationship with geometry (notably, symplectic geometry and Poisson structures) and serves as a link between classical...
    53 KB (9,323 words) - 04:39, 26 May 2025
  • theorems: Gromov's compactness theorem (geometry) in Riemannian geometry Gromov's compactness theorem (topology) in symplectic topology Gromov's Betti number theorem [ru]...
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  • complex geometry leading to the Borel–Weil–Bott theorem, or in symplectic geometry, where Kähler manifolds are symplectic, in Riemannian geometry where...
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  • Arnold conjecture (category Symplectic geometry)
    symplectic geometry, a branch of differential geometry. Let ( M , ω ) {\displaystyle (M,\omega )} be a closed (compact without boundary) symplectic manifold...
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  • Thumbnail for Alan Weinstein
    cover many areas in differential geometry and mathematical physics, including Riemannian geometry, symplectic geometry, Lie groupoids, geometric mechanics...
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  • particularly in representation theory, a symplectic resolution is a morphism that combines symplectic geometry and resolution of singularities. Let π :...
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  • In mathematics, a symplectic matrix is a 2 n × 2 n {\displaystyle 2n\times 2n} matrix M {\displaystyle M} with real entries that satisfies the condition...
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  • Gromov–Witten invariant (category Symplectic topology)
    In mathematics, specifically in symplectic topology and algebraic geometry, Gromov–Witten (GW) invariants are rational numbers that, in certain situations...
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  • Darboux's theorem (category Symplectic geometry)
    fields, the chief among them being symplectic geometry. Indeed, one of its many consequences is that any two symplectic manifolds of the same dimension are...
    10 KB (1,377 words) - 11:08, 25 May 2025