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Longer titles found: Almost symplectic manifold (view)

searching for Symplectic manifold 21 found (130 total)

Weinstein conjecture (781 words) [view diff] exact match in snippet view article find links to article

that any contact manifold (M,α) can be embedded into a canonical symplectic manifold, called the symplectization of M, such that M is a contact type level

Gromov's compactness theorem (topology) (272 words) [view diff] exact match in snippet view article

to vary. Usually, the energy bound is achieved by considering a symplectic manifold with compatible almost-complex structure as the target, and assuming

Batalin–Vilkovisky formalism (3,114 words) [view diff] exact match in snippet view article find links to article

bi-vector π i j {\displaystyle \pi ^{ij}} is invertible, one has an odd symplectic manifold. In that case, there exists an odd Darboux Theorem. That is, there

Quantization (physics) (1,523 words) [view diff] exact match in snippet view article

★-product is taken to be a deformation of the algebra of functions on a symplectic manifold or Poisson manifold. However, as a natural quantization scheme (a

Hyperkähler manifold (1,641 words) [view diff] exact match in snippet view article find links to article

Calabi conjecture implies that a compact, Kähler, holomorphically symplectic manifold ( M , I , Ω ) {\displaystyle (M,I,\Omega )} is always equipped with

Contact geometry (2,430 words) [view diff] exact match in snippet view article find links to article

contact manifold M, the product M×R has a natural structure of a symplectic manifold. If α is a contact form on M, then ω = d(etα) is a symplectic form

Glossary of symplectic geometry (554 words) [view diff] exact match in snippet view article find links to article

form The volume form ω n / n ! {\displaystyle \omega ^{n}/n!} on a symplectic manifold ( M , ω ) {\displaystyle (M,\omega )} of dimension 2n. Maslov index

A∞-operad (603 words) [view diff] exact match in snippet view article find links to article

A_{\infty }} -algebra. Examples feature the Fukaya category of a symplectic manifold, when it can be defined (see also pseudoholomorphic curve). The most

Perfect obstruction theory (596 words) [view diff] exact match in snippet view article find links to article

obstruction theory in a canonical way. Example: Let M be a complex symplectic manifold. Then the (scheme-theoretic) intersection of Lagrangian submanifolds

Kaoru Ono (521 words) [view diff] exact match in snippet view article find links to article

University (KURIMS). On the Arnold conjecture for weakly monotone symplectic manifold, Vol. 119, 1995, pp. 519–537 doi:10.1007/BF01245191 with Fukaya:

Fundamental vector field (1,033 words) [view diff] exact match in snippet view article find links to article

closely related idea is that of Hamiltonian vector fields. Given a symplectic manifold ( M , ω ) {\displaystyle (M,\omega )} , we say that X H {\displaystyle

Geometric mechanics (995 words) [view diff] exact match in snippet view article find links to article

}=\mathbf {J} ^{-1}(\mu )/G_{\mu }} , and this reduced space is a symplectic manifold if μ {\displaystyle \mu } is a regular value of J. Hamilton's principle

Kenji Fukaya (690 words) [view diff] exact match in snippet view article find links to article

category of whose objects are Lagrangian submanifolds of a given symplectic manifold, is named after him, and is intimately related to Floer homology

Homotopy principle (1,722 words) [view diff] exact match in snippet view article find links to article

be reduced to topology. As an example, embedded Lagrangians in a symplectic manifold do not satisfy an h-principle, to prove this one can for instance

Simon Donaldson (2,039 words) [view diff] exact match in snippet view article find links to article

of the Donaldson invariant (or instanton invariants). Any compact symplectic manifold admits a symplectic Lefschetz pencil (Donaldson 1999). Donaldson's

Valya algebra (751 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \alpha =F_{k}(x)\,dx^{k},\quad \beta =G_{k}(x)\,dx^{k}} on a symplectic manifold can be introduced by the rule ( α , β ) 0 = d Ψ ( α , β ) + Ψ ( d

Toric variety (2,228 words) [view diff] exact match in snippet view article find links to article

moment map for the action of U ( 1 ) {\displaystyle U(1)} on the symplectic manifold C P 2 {\displaystyle \mathbb {CP} ^{2}} . From the fundamental theorem

Measure (mathematics) (5,554 words) [view diff] exact match in snippet view article

below. Liouville measure, known also as the natural volume form on a symplectic manifold, is useful in classical statistical and Hamiltonian mechanics. Gibbs

Generalized complex structure (3,145 words) [view diff] exact match in snippet view article find links to article

complex manifold is, up to diffeomorphism and B-field, a product of a symplectic manifold with a generalized complex manifold which is of complex type at the

Janusz Grabowski (2,242 words) [view diff] exact match in snippet view article find links to article

Grabowski (1990). "Homomorphisms of the Lie algebras associated with a symplectic manifold". Compositio Mathematica (in French). 76 (3): 315–349. ISSN 1570-5846

Timeline of manifolds (1,178 words) [view diff] exact match in snippet view article find links to article

Kontsevich Formulates homological mirror symmetry conjecture: X a compact symplectic manifold with first chern class c1(X) = 0 and Y a compact Calabi–Yau manifold