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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 paper, the Cauchy problem for equivariant wave maps from 3 + 1 Minkowski spacetime into the 3-sphere was studied numerically and two conjectures about the threshold of singularity formation were formulated.
Abstract: We study numerically the Cauchy problem for equivariant wave maps from 3 + 1 Minkowski spacetime into the 3-sphere. On the basis of numerical evidence combined with stability analysis of self-similar solutions we formulate two conjectures. The first conjecture states that singularities which are produced in the evolution of sufficiently large initial data are approached in a universal manner given by the profile of a stable self-similar solution. The second conjecture states that the codimension-one stable manifold of a self-similar solution with exactly one instability determines the threshold of singularity formation for a large class of initial data. Our results can be considered as a toy-model for some aspects of the critical behaviour in the formation of black holes.
56 citations
TL;DR: In this article, a general genericity and stability theorem for bifurcation diagrams in equivariant bifurbcation theory is proved for all compact Lie groups and absolutely irreducible G-representations.
Abstract: A study is made of the failure of the Maximal Isotropy Subgroup Conjecture for the Weyl group seriesW(D)
k
. As part of the investigation, a general genericity and stability theorem is proved for bifurcation diagrams in equivariant bifurcation theory. As well, a concept of determinacy for equivariant bifurcation theory is introduced and it is shown that, for all compact Lie groupsG and absolutely irreducibleG-representationsV, G-equivariant bifurcation problems onV are finitely determined.
56 citations
TL;DR: A rational analysis of methods which use symmetry to enlarge the ensemble size of a data set and provides sufficient conditions for numerical schemes, based on the linear and the nonlinear Galerkin method, to retain the symmetries of the original system.
55 citations
TL;DR: The theory of principal G-bundles over a Lie groupoid is an important one unifying various types of principal bundles, including those over manifolds, those over orbifolds, as well as equivariant principal bundles.
Abstract: The theory of principal G-bundles over a Lie groupoid is an important one unifying various types of principal G-bundles, including those over manifolds, those over orbifolds, as well as equivariant principal G-bundles. In this paper, we study differential geometry of these objects, including connections and holonomy maps. We also introduce a Chern–Weil map for these principal bundles and prove that the characteristic classes obtained coincide with the universal characteristic classes. As an application, we recover the equivariant Chern–Weil map of Bott–Tu. We also obtain an explicit chain map between the Weil model and the simplicial model of equivariant cohomology which reduces to the Bott–Shulman map $$S(\mathfrak{g}^*)^G \to H^*(BG)$$
when the manifold is a point.
55 citations
TL;DR: In this paper, it was shown that the coherent-constructible correspondence of a complete toric variety is compatible with T-duality in the sense that τ = μ ∘ κ.
55 citations