Topic
Symplectic vector space
About: Symplectic vector space is a research topic. Over the lifetime, 2048 publications have been published within this topic receiving 53456 citations.
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TL;DR: In this paper, the sine-Gordon equation is considered in the Hamiltonian framework provided by the Adler-Kostant-Symes theorem, and real quasiperiodic solutions are computed in terms of theta functions using a Liouville generating function which generates a canonical transformation to linear coordinates on the Jacobi variety of a suitable hyperelliptic curve.
Abstract: The sine‐Gordon equation is considered in the Hamiltonian framework provided by the Adler–Kostant–Symes theorem. The phase space, a finite dimensional coadjoint orbit in the dual space g* of a loop algebra g , is parameterized by a finite dimensional symplectic vector space W embedded into g* by a moment map. Real quasiperiodic solutions are computed in terms of theta functions using a Liouville generating function which generates a canonical transformation to linear coordinates on the Jacobi variety of a suitable hyperelliptic curve.
13 citations
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TL;DR: In this article, the rank and discriminant of the Picard group on a K3 surface X has been computed using moduli spaces of K3 surfaces with symplectic G-action.
Abstract: We consider the symplectic action of a finite group G on a K3 surface X. The Picard group of X has a primitive sublattice determined by G. We show how to compute the rank and discriminant of this sublattice. We then investigate the classification of symplectic actions by a fixed finite group, using moduli spaces of K3 surfaces with symplectic G-action.
13 citations
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TL;DR: The rational blow-down procedure as mentioned in this paper replaces the tubular neighbourhood of a string of 2-spheres (intersecting each other according to the linear plumbing tree with framings specified by the continued fraction coefficients of − p 2 pq−1 for some p, q relatively prime) with a rational homology disk.
Abstract: The rational blow-down procedure (introduced by Fintushel and Stern [4] and generalized by Park [25]) turned out to be one of the most effective operations in constructing smooth 4-manifolds with interesting topological properties, cf. [5, 26–28]. Recall that when performing the rational blow-down operation we simply replace the tubular neighbourhood of a string of 2-spheres (intersecting each other according to the linear plumbing tree with framings specified by the continued fraction coefficients of − p 2 pq−1 for some p, q relatively prime) with a rational homology disk. The success of this operation might be explained by the fact that—as Symington showed [30, 31]—it can be performed symplectically. More precisely, if the ambient 4-manifold is symplectic and the spheres are symplectic submanifolds intersecting each other orthogonally then the neighbourhood
13 citations
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TL;DR: In this article, the authors analyse certain cofibrations of projective spaces in terms of Thorn complexes of Spin bundles, and by applying the symplectic cobordism functor they are able to deduce new relations amongst the elements 0t in the bordism ring.
Abstract: We analyse certain cofibrations of projective spaces in terms of Thorn complexes of Spin bundles, and by applying the symplectic cobordism functor we are able to deduce new relations amongst the elements 0t in the symplectic bordism ring.
13 citations
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TL;DR: Using Seiberg-Witten theory and spectral sequences, this paper proved that the total space of a locally trivial torus bundle over a surface Σg of genus g > 1 carries a symplectic structure if and only if the homology class of the fiber [T2] is nonzero in H2(E, ℝ).
Abstract: Let E be the total space of a locally trivial torus bundle over a surface Σg of genus g > 1. Using Seiberg–Witten theory and spectral sequences, we prove that E carries a symplectic structure if and only if the homology class of the fiber [T2] is nonzero in H2(E, ℝ).
13 citations