منابع مشابه
Symplectic cohomologies on phase space
The phase space of a particle or a mechanical system contains an intrinsic symplectic structure, and hence, it is a symplectic manifold. Recently, new invariants for symplectic manifolds in terms of cohomologies of differential forms have been introduced by Tseng and Yau. Here, we discuss the physical motivation behind the new symplectic invariants and analyze these invariants for phase space, ...
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In joint work with S.-T. Yau, we construct new cohomologies of differential forms and elliptic operators on symplectic manifolds. Their construction can be described simply following a symplectic decomposition of the exterior derivative operator into two first-order differential operators, which are analogous to the Dolbeault operators in complex geometry. These first-order operators lead to ne...
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Let Y be an affine symplectic variety of dimension 2n, and let π : X → Y be a crepant resolution. By the definition, there is a symplectic 2-form σ̄ on the smooth part Yreg ∼= π (Yreg), and it extends to a 2-form σ on X. Since π is crepant, σ is a symplectic 2-form on X. The symplectic structures on X and Y define Poisson structures on them in a natural manner. One can define a Poisson deformati...
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ژورنال
عنوان ژورنال: Bollettino dell'Unione Matematica Italiana
سال: 2018
ISSN: 1972-6724,2198-2759
DOI: 10.1007/s40574-018-0175-z