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, a curvature inequality for SO(3)-bundle with connection was studied for manifolds with dimension four, where the base has dimension four and the manifold is a manifold with dimension c 1 = 0.
Abstract: Given an SO(3)-bundle with connection, the associated two- sphere bundle carries a natural closed 2-form. Asking that this be symplectic gives a curvature inequality first considered by Rezn- ikov [34]. We study this inequality in the case when the base has dimension four, with three main aims. Firstly, we use this approach to construct symplectic six-manifolds with c 1 =0 which are never Kahler; e.g., we produce such manifolds with b 1 = 0 = b 3 and also with c 2 [w]
47 citations
TL;DR: Symplectic algorithms are numerical integrators for Hamiltonian systems that preserve the symplectic structure in phase space as discussed by the authors, and they tend to perform better than their nonsymplectic counterparts.
47 citations
TL;DR: In this article, the irreducible complex characters of the symplectic groups Sp 2n (q) and the orthogonal groups, Spin 2n+1(q) of degrees up to the bound D were classified.
Abstract: We classify the irreducible complex characters of the symplectic groups Sp 2n (q) and the orthogonal groups , Spin 2n+1(q) of degrees up to the bound D, where D = (q n − 1)q 4n−10/2 for symplectic groups, D = q 4n−8 for orthogonal groups in odd dimension, and D = q 4n−10 for orthogonal groups in even dimension.
47 citations
47 citations
TL;DR: In this article, a general method for the construction of non-formal symplectic manifolds with non-trivial Massey products of arbitrarily high order is proposed, which uses symplectic blow-up.
Abstract: Massey products in symplectic manifolds are studied. A general method for the construction of symplectic manifolds with non-trivial Massey products of arbitrarily high order is put forward. This method uses symplectic blow-up. The authors find conditions guaranteeing that the symplectic blow-up of X along a submanifold Y inherits non-trivial Massey products from X and Y. As a result, a general construction of non-formal symplectic manifolds by means of symplectic blow-ups is developed.
47 citations