English
symplectic
Adjective

symplectic (not comparable)

  1. Placed in or among, as if woven together.
  2. (group theory, of a group) Whose characteristic abelian subgroups are cyclic.
  3. (mathematics, multilinear algebra, of a bilinear form) That is alternating and nondegenerate.
  4. (mathematics, multilinear algebra, of a vector space) That is equipped with an alternating nondegenerate bilinear form.
  5. (mathematics) Of or pertaining to (the geometry of) a differentiable manifold equipped with a closed nondegenerate bilinear form.
    • 1995, V. I. Arnold, Some remarks on symplectic monodromy of Milnor fibrations, Helmut Hofer, Clifford H. Taubes, Alan Weinstein, Eduard Zehnder (editors), The Floer Memorial Volume, Birkhäuser Verlag, page 99 ↗,
      There exist interesting and unexplored relations between symplectic geometry and the theory of critical points of holomorphic functions.
    • 1997, C. H. Cushman-de Vries (translator), Richard H. Cushman, Gijs M. Tuynman (translation editors), Jean-Marie Souriau, Structure of Dynamical Systems: A Symplectic View of Physics, Springer Science & Business Media (Birkhäuser).
    • 2003, Fabrizio Catanese, Gang Tian (editors), Symplectic 4-Manifolds and Algebraic Surfaces: Lectures given at the C.I.M.E Summer School ↗, Springer, Lecture Notes in Mathematics No. 1938.
    • 2003, Yakov Eliashberg, Boris A. Khesin, François Lalonde (editors), Symplectic and Contact Topology: Interactions and Perspectives ↗, American Mathematical Society.
    • 2003, Maung Min-Oo, The Dirac Operator in Geometry and Physics, Steen Markvorsen, Maung Min-Oo (editors), Global Riemannian Geometry: Curvature and Topology, Springer, page 72 ↗,
      In symplectic geometry, there is a notion of fibrations \pi : P \rightarrow M with a symplectic manifold F as fiber, where the structure group is the group of (exact) Hamiltonian symplectomorphisms of the fiber. These are called symplectic fibrations. If the base manifold (M,\omega_M) is also symplectic, there is a weak coupling construction, originally due to Thurston, of defining a symplectic structure on the total space P.
  6. That moves in the same direction as a system of synchronized waves.
  7. (petrology, mineralogy) Of or pertaining to a symplectite; symplectitic.
Antonyms Related terms Noun

symplectic (plural symplectics)

  1. (mathematics) A symplectic bilinear form, manifold, geometry, etc.
    • 1967, Indiana University Mathematics Journal, Volume 16, Issue 1, Indiana University, page 339 ↗,
      The structure of stable symplectics on finite dimensional spaces has been studied by Krein [8], Gelfand & Lidskii [9], and Moser [10] in work of considerable practical importance.
  2. (ichthyology) A bone in the teleostean fishes that forms the lower ossification of the suspensorium, and which articulates below with the quadrate bone by which it is firmly held.
    • 1914, The Philippine Journal of Science, Volume 9, page 27 ↗,
      The symplectics (9) consist of a somewhat curved central triangular portion with the base upward, and anteriorly and posteriorly from this extends a wing-like process.
    • 1965, Agra University Journal of Research: Science, Volume 14, page 71 ↗,
      The symplectics (Fig. 8, sym) are thin slender bones placed vertically in between the quadrates and the hyomandibulars.
    • 1967, Tyson R. Roberts, Studies on the Osteology and Phylogeny of Characoid Fishes, page 59 ↗,
      In many teleosts, on the other hand, including the catfishes, the symplectics have been entirely lost.


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