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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 authors construct explicit BPS and non-BPS solutions of the Yang-Mills equations on the noncommutative space R^{2n}_\theta x S^2 which have manifest spherical symmetry.
Abstract: We construct explicit BPS and non-BPS solutions of the Yang-Mills equations on the noncommutative space R^{2n}_\theta x S^2 which have manifest spherical symmetry. Using SU(2)-equivariant dimensional reduction techniques, we show that the solutions imply an equivalence between instantons on R^{2n}_\theta x S^2 and nonabelian vortices on R^{2n}_\theta, which can be interpreted as a blowing-up of a chain of D0-branes on R^{2n}_\theta into a chain of spherical D2-branes on R^{2n} x S^2. The low-energy dynamics of these configurations is described by a quiver gauge theory which can be formulated in terms of new geometrical objects generalizing superconnections. This formalism enables the explicit assignment of D0-brane charges in equivariant K-theory to the instanton solutions.
59 citations
01 Feb 1984
TL;DR: In this paper, the authors give an exposition of the various triviality theorems, the equivariant version of a result due to L. Brown, and a simplification of the proof of Kasparov's triviality theorem.
Abstract: The purpose of this paper is to give an exposition of the various triviality theorems, the equivariant version of a result due to L. Brown, and a simplification of the proof of Kasparov's triviality theorems.
59 citations
TL;DR: In this paper, the Ray-Singer analytic torsion of the trivial line bundle on an Enriques surface with Ricci-flat Kahler metric is given by the value of the norm of the Borcherds Φ-function at its period point.
Abstract: In this paper, we introduce an invariant of a K3 surface with ℤ2-action equipped with a ℤ2-invariant Kahler metric, which we obtain using the equivariant analytic torsion of the trivial line bundle. This invariant is shown to be independent of the choice of the Kahler metric. It can be viewed as a function on the moduli space of K3 surfaces with involution. The main result of this paper is that this function can be identified with an automorphic form, which characterizes the discriminant locus. In particular, we show that the Ray–Singer analytic torsion of the trivial line bundle on an Enriques surface with Ricci-flat Kahler metric is given by the value of the norm of the Borcherds Φ-function at its period point.
59 citations
59 citations
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TL;DR: In this paper, the notion of Poincar´e duality in KK-theory was extended to the setting of quantum group actions, and an important ingredient in this approach is the replacement of ordinary tensor products by braided tensor product.
Abstract: We extend the notion of Poincar\'e duality in KK-theory to the setting of quantum group actions. An important ingredient in our approach is the replacement of ordinary tensor products by braided tensor products. Along the way we discuss general properties of equivariant KK-theory for locally compact quantum groups, including the construction of exterior products. As an example, we prove that the standard Podle\'s sphere is equivariantly Poincar\'e dual to itself.
59 citations