Definition of "symplectic"

symplectic

/sɪmˈplɛktɪk/

adjective
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.
  Quotations
  There exist interesting and unexplored relations between symplectic geometry and the theory of critical points of holomorphic functions.
  1995, V. I. Arnold, “Some remarks on symplectic monodromy of Milnor fibrations”, in Helmut Hofer, Clifford H. Taubes, Alan Weinstein, Eduard Zehnder, editors, The Floer Memorial Volume, Birkhäuser Verlag, page 99
  2003, Yakov Eliashberg, Boris A. Khesin, François Lalonde, editors, Symplectic and Contact Topology: Interactions and Perspectives, American Mathematical Society
  In symplectic geometry, there is a notion of fibrations π : P → M {\displaystyle \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 , ω M ) {\displaystyle (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 {\displaystyle P} .
  2003, Maung Min-Oo, “The Dirac Operator in Geometry and Physics”, in Steen Markvorsen, Maung Min-Oo, editors, Global Riemannian Geometry: Curvature and Topology, Springer, page 72
6. That moves in the same direction as a system of synchronized waves.
7. (petrology, mineralogy) Of or pertaining to a symplectite; symplectitic.
noun
plural symplectics
1. (mathematics) A symplectic bilinear form, manifold, geometry, etc.
  Quotations
  The structure of stable symplectics on finite dimensional spaces has been studied by Krein , Gelfand & Lidskii , and Moser in work of considerable practical importance.
  1967, Journal of Mathematics and Mechanics, volume 16, number 1, Indiana University, page 339
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.
  Quotations
  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.
  1914, The Philippine Journal of Science, Volume 9, page 27
  The symplectics (Fig. 8, sym) are thin slender bones placed vertically in between the quadrates and the hyomandibulars.
  1965, Agra University Journal of Research: Science, Volume 14, page 71
  In many teleosts, on the other hand, including the catfishes, the symplectics have been entirely lost.
  1967, Tyson R. Roberts, Studies on the Osteology and Phylogeny of Characoid Fishes, page 59

Definition of "symplectic"

symplectic

adjective

Quotations

noun

Quotations

Quotations