Topic
Equivariant map
About: Equivariant map is a research topic. Over the lifetime, 9205 publications have been published within this topic receiving 137115 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, the existence and uniqueness of equivariant momentum mappings for Poisson actions of Poisson Lie groups is analyzed. But the existence problem is solved under some extra hypotheses, for example, when the action preserves the Poisson structure, and it is shown that this action is trivial whenever the group is compact or semisimpleteness.
Abstract: We analyze the question of existence and uniqueness of equivariant momentum mappings for Poisson actions of Poisson Lie groups. A necessary and sufficient condition for the equivariant momentum mapping to be unique is given. The existence problem is solved under some extra hypotheses, for example, when the action preserves the Poisson structure. In this case, the problem is closely related to the triviality of the induced group action on the Poisson cohomology. This action is shown to be trivial whenever the group is compact or semisimple. Conceptually, these results rely upon a version of “Poisson calculus” developed here to make one-forms on a Poisson manifold induce a “flow” preserving the Poisson structure. In the general case, obstructions to the existence of an infinitesimal version of an equivariant momentum mapping are found. Using Lie algebra cohomology with coefficients in Frechet modules, we show that the obstructions vanish, and the infinitesimal mapping exists, when the group is compact semisimple. We also prove the rigidity of compact group actions preserving the Poisson structure on a compact manifold and calculate the Poisson cohomology of the Poisson homogeneous space .
42 citations
TL;DR: In this paper, a quantum version of the Kirwan map is constructed from the equivariant quantum cohomology QH (X/G) of a smooth polarized complex projective variety X with the action of a connected complex reductive group G to the orbifold quantum cohology Q H(X//G).
Abstract: This is the second in a sequence of papers in which we construct a quantum version of the Kirwan map from the equivariant quantum cohomology QH
G
(X) of a smooth polarized complex projective variety X with the action of a connected complex reductive group G to the orbifold quantum cohomology QH(X//G) of its geometric invariant theory quotient X//G, and prove that it intertwines the genus zero gauged Gromov–Witten potential of X with the genus zero Gromov–Witten graph potential of X//G. In this part we construct virtual fundamental classes on the moduli spaces used in the construction of the quantum Kirwan map and the gauged Gromov–Witten potential.
42 citations
TL;DR: In this paper, the moduli stack of toric vector bundles with fixed equivariant total Chern class is presented as a quotient of a fine moduli scheme of framed bundles by a linear group action.
Abstract: We give a presentation of the moduli stack of toric vector bundles with fixed equivariant total Chern class as a quotient of a fine moduli scheme of framed bundles by a linear group action. This fine moduli scheme is described explicitly as a locally closed subscheme of a product of partial flag varieties cut out by combinatorially specified rank conditions. We use this description to show that the moduli of rank three toric vector bundles satisfy Murphy’s law, in the sense of Vakil. The preliminary sections of the paper give a selfcontained introduction to Klyachko’s classification of toric vector bundles.
42 citations
Posted Content•
TL;DR: This paper studied connections between generalized moonshine and elliptic cohomology with a focus on the action of the Hecke correspondence and its implications for the notion of replicability.
Abstract: This paper studies connections between generalized moonshine and elliptic cohomology with a focus on the action of the Hecke correspondence and its implications for the notion of replicability.
42 citations
01 Jan 2003
TL;DR: In this article, the authors present a compendium to a series of lectures concerning the topological aspects of the Baum-Connes Conjecture, where the left hand side of the equation K * G (E G) ≅ K * top (C r * (G)) is considered.
Abstract: These notes are a compendium to a series of lectures concerning the topological aspects of the Baum-Connes Conjecture — the left hand side of the equation K * G (E G) ≅ K * top (C r * (G)) — the equivariant K-homology of E G. Besides of a presentation of the material needed to compute * G (E G,the reader will find an extensive discussion of many conjectures related to the Baum-Connes Conjecture.
42 citations