symplectic

1. not comparablePlaced in or among, as if woven together.
2. not comparablegroup theoryWhose characteristic abelian subgroups are cyclic.
3. not comparablemultilinear algebramathematicsThat is alternating and nondegenerate.
4. not comparablemultilinear algebramathematicsThat is equipped with an alternating nondegenerate bilinear form.
5. not comparablemathematicsOf or pertaining to (the geometry of) a differentiable manifold equipped with a closed nondegenerate bilinear form.

   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.

   3 more examples

   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

   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).

   In symplectic geometry, there is a notion of fibrations #92;pi#58;P#92;rightarrowM 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,#92;omega#95;M) is also symplectic, there is a weak coupling construction, originally due to Thurston, of defining a symplectic structure on the total space 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. not comparableThat moves in the same direction as a system of synchronized waves.
7. not comparablechemistryOf or pertaining to a symplectite; symplectitic.

plural symplectics

1. mathematicsA symplectic bilinear form, manifold, geometry, etc.

   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.

   1967, Journal of Mathematics and Mechanics, volume 16, number 1, Indiana University, page 339

2. biologyA 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.

   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

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   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