This is a glossary of properties and concepts in
symplectic geometry
Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic geometry has its origins in the ...
in mathematics. The terms listed here cover the occurrences of symplectic geometry both in
topology
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ho ...
as well as in
algebraic geometry (over the
complex number
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the for ...
s for definiteness). The glossary also includes notions from
Hamiltonian geometry,
Poisson geometry
In differential geometry, a Poisson structure on a smooth manifold M is a Lie bracket \ (called a Poisson bracket in this special case) on the algebra (M) of smooth functions on M , subject to the Leibniz rule
: \ = \h + g \ .
Equivalentl ...
and
geometric quantization
In mathematical physics, geometric quantization is a mathematical approach to defining a quantum theory corresponding to a given classical theory. It attempts to carry out quantization, for which there is in general no exact recipe, in such a way ...
.
In addition, this glossary also includes some concepts (e.g., virtual fundamental class) in
intersection theory
In mathematics, intersection theory is one of the main branches of algebraic geometry, where it gives information about the intersection of two subvarieties of a given variety. The theory for varieties is older, with roots in Bézout's theorem o ...
that appear in symplectic geometry as they do not naturally fit into other lists such as the
glossary of algebraic geometry
This is a glossary of algebraic geometry.
See also glossary of commutative algebra, glossary of classical algebraic geometry, and glossary of ring theory. For the number-theoretic applications, see glossary of arithmetic and Diophantine geometry. ...
.
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Notes
References
*
*Kontsevich, M. Enumeration of rational curves via torus actions. Progr. Math. 129, Birkhauser, Boston, 1995.
*Meinrenken'
lecture notes on symplectic geometry*
*
External links
*http://arxiv.org/pdf/1409.0837.pdf (tangentially related)
{{differential-geometry-stub
Symplectic geometry
Symplectic
Wikipedia glossaries using description lists