Geometric and Algebraic Reduction for Singular Momentum Maps
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In this article, the singular constraint sets of symplectic manifolds are reduced by vanishing of a momentum map associated to the Hamiltonian action of a compact Lie group, and a necessary and sufficient condition for them to agree is derived.About:
This article is published in Advances in Mathematics.The article was published on 1990-01-01 and is currently open access. It has received 90 citations till now. The article focuses on the topics: Moment map & Lie group.read more
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Stratified symplectic spaces and reduction
Reyer Sjamaar,Eugene Lerman +1 more
TL;DR: In this paper, it was shown that if the regularity assumptions are dropped, the space MO is a union of symplectic manifolds, i.e., it is a stratified symplectic space.
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The symplectic geometry of polygons in Euclidean space
Michael Kapovich,John J. Millson +1 more
TL;DR: In this article, the authors studied the symplectic geometry of moduli spaces M r of polygons with xed side lengths in Euclidean space and showed that M r has a natural structure of a complex analytic space and is complex-analytically isomorphic to the weighted quotient of (S 2) n constructed by Deligne and Mostow.
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Momentum maps and classical relativistic fields. Part 1: Covariant Field Theory
TL;DR: In this article, the Lagrangian and Hamiltonian structure of classical field theories with constraints is studied, and the connections between initial value constraints and gauge transformations in such theories are explored.
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A Universal Reduction Procedure for Hamiltonian Group Actions
TL;DR: In this article, a universal method of inducing a Poisson structure on a singular reduced space from the Poisson structures on the orbit space for the group action is given. But it is not shown that the resulting structure is non-degenerate.
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Rieffel induction as generalized quantum Marsden-Weinstein reduction
TL;DR: In this article, a new approach to quantization of constrained or otherwise reduced classical mechanical systems is proposed, based on the generalized symplectic reduction procedure of Mikami and Weinstein, as further extended by Xu in connection with symplectic equivalence bimodules and Morita equivalence of Poisson manifolds.
References
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Book
Foundations of mechanics
TL;DR: In this article, Ratiu and Cushman introduce differential theory calculus on manifolds and derive an overview of qualitative and topological properties of differentiable properties of topological dynamics.
Book
Singular points of complex hypersurfaces
TL;DR: The Singular Points of Complex Hypersurfaces (AM-61) as mentioned in this paper is a seminal work in the area of complex hypersurfaces, and is based on as mentioned in this paper.