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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 behavior in formation of black holes.
42 citations
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TL;DR: The projection body operator π is invariant under translations and equivariant under rotations, and it is known that π maps the set of polytopes in Rn into itself.
Abstract: The projection body operator \Pi, which associates with every convex body in Euclidean space Rn its projection body, is a continuous valuation, it is invariant under translations and equivariant under rotations. It is also well known that \Pi\ maps the set of polytopes in Rn into itself. We show that \Pi\ is the only non-trivial operator with these properties.
42 citations
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TL;DR: In this article, the authors describe some models of twisted equivariant / ("-theory, both topological and geometric, and state a theorem which relates representa- tions of loop groups to twisted equivariant /"theory.
Abstract: Twisted /("-theory has received much attention recently in both math ematics and physics. We describe some models of twisted /("-theory, both topological and geometric. Then we state a theorem which relates representa tions of loop groups to twisted equivariant /("-theory. This is joint work with Michael Hopkins and Constantin Teleman.
42 citations
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TL;DR: In this article, it was shown that a complex normal projective variety has non-positive Kodaira dimension if it admits a non-isomorphic quasi-polarized endomorphism.
Abstract: It is shown that a complex normal projective variety has non-positive Kodaira dimension if it admits a non-isomorphic quasi-polarized endomorphism. The geometric structure of the variety is described by methods of equivariant lifting and fibrations. (For endomorphisms of projective spaces, see version 1).
42 citations
TL;DR: In this paper, the authors construct some classes of dynamical r-matrices over a nonabelian base and quantize some of them by constructing dynamical (pseudo)twists in the sense of Xu.
Abstract: We construct some classes of dynamical r-matrices over a nonabelian base, and quantize some of them by constructing dynamical (pseudo)twists in the sense of Xu. This way, we obtain quantizations of r-matrices obtained in earlier work of the second author with Schiffmann and Varchenko. A part of our construction may be viewed as a generalization of the Donin-Mudrov nonabelian fusion construction. We apply these results to the construction of equivariant star-products on Poisson homogeneous spaces, which include some homogeneous spaces introduced by De Concini.
42 citations