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Equivariant map
About: Equivariant map is a research topic. Over the lifetime, 9205 publications have been published within this topic receiving 137115 citations.
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TL;DR: In this article, the authors show equivalence of pure point diffraction and pure point dynamical spectrum for measurable dynamical systems build from locally finite measures on locally compact Abelian groups.
Abstract: We show equivalence of pure point diffraction and pure point dynamical spectrum for measurable dynamical systems build from locally finite measures on locally compact Abelian groups. This generalizes all earlier results of this type. Our approach is based on a study of almost periodicity in a Hilbert space. It allows us to set up a perturbation theory for arbitrary equivariant measurable perturbations.
51 citations
TL;DR: In this paper, Klyachko and Perling developed a combinatorial description of pure equivariant sheaves of any dimension on an arbitrary nonsingular toric variety X.
51 citations
01 Feb 1996
TL;DR: In this article, a simple simple Poisson-Lie group equipped with a Poisson structure P and (M, omega) being a symplectic manifold is considered, and the moment map is an equivariant moment map in the sense of Lu and Weinstein which maps
Abstract: Let G(P) be a compact simple Poisson-Lie group equipped with a Poisson structure P, and (M, omega) be a symplectic manifold. Assume that M carries a Poisson action of G(P), and there is an equivariant moment map in the sense of Lu and Weinstein which maps
51 citations
TL;DR: In this article, the authors define the notion of an "equivariant" Lagrangian submanifold, which roughly corresponds to equivariant coherent sheaves under mirror symmetry.
Abstract: Given a symplectic cohomology class of degree 1, we define the notion of an “equivariant" Lagrangian submanifold (this roughly corresponds to equivariant coherent sheaves under mirror symmetry). The Floer cohomology of equivariant Lagrangian submanifolds has a natural endomorphism, which induces an $${\mathbb{R}}$$
-grading by generalized eigenspaces. Taking Euler characteristics with respect to the induced grading yields a deformation of the intersection number. Dehn twists act naturally on equivariant Lagrangians. Cotangent bundles and Lefschetz fibrations give fully computable examples. A key step in computations is to impose the “dilation" condition stipulating that the BV operator applied to the symplectic cohomology class gives the identity.
51 citations
TL;DR: In this paper, the authors construct triples of commuting real structures on the moduli space of Higgs bundles, whose fixed loci are branes of type (B, A, A), (A, B, A).
Abstract: We construct triples of commuting real structures on the moduli space of Higgs bundles, whose fixed loci are branes of type (B, A, A), (A, B, A) and (A, A, B). We study the real points through the associated spectral data and describe the topological invariants involved using KO, KR and equivariant K-theory.
51 citations