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
Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...
as well as in
algebraic geometry
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...
(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 field in mathematics, a Poisson manifold is a smooth manifold endowed with a Poisson structure. The notion of Poisson manifold generalises that of symplectic manifold, which in turn generalises the phase space from Hami ...
and
geometric quantization.
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.
A
C
D
E
F
H
I
K
L
M
N
P
Q
S
T
V
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