Topic
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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Book•
28 Jun 1994
TL;DR: In this paper, the DG-modules and equivariant cohomology of toric varieties have been studied, and the derived category D G (X) and functors have been defined.
Abstract: Derived category D G (X) and functors.- DG-modules and equivariant cohomology.- Equivariant cohomology of toric varieties.
604 citations
587 citations
TL;DR: In this article, a principal ℝ + 5 -bundle over the usual Teichmuller space of ans times punctured surface is introduced, and several coordinatizations of the total space of the bundle are developed.
Abstract: A principal ℝ
+
5
-bundle over the usual Teichmuller space of ans times punctured surface is introduced. The bundle is mapping class group equivariant and admits an invariant foliation. Several coordinatizations of the total space of the bundle are developed. There is furthermore a natural cell-decomposition of the bundle. Finally, we compute the coordinate action of the mapping class group on the total space; the total space is found to have a rich (equivariant) geometric structure. We sketch some connections with arithmetic groups, diophantine approximations, and certain problems in plane euclidean geometry. Furthermore, these investigations lead to an explicit scheme of integration over the moduli spaces, and to the construction of a “universal Teichmuller space,” which we hope will provide a formalism for understanding some connections between the Teichmuller theory, the KP hierarchy and the Virasoro algebra. These latter applications are pursued elsewhere.
561 citations
Posted Content•
TL;DR: Tensor field neural networks are introduced, which are locally equivariant to 3D rotations, translations, and permutations of points at every layer, and demonstrate the capabilities of tensor field networks with tasks in geometry, physics, and chemistry.
Abstract: We introduce tensor field neural networks, which are locally equivariant to 3D rotations, translations, and permutations of points at every layer. 3D rotation equivariance removes the need for data augmentation to identify features in arbitrary orientations. Our network uses filters built from spherical harmonics; due to the mathematical consequences of this filter choice, each layer accepts as input (and guarantees as output) scalars, vectors, and higher-order tensors, in the geometric sense of these terms. We demonstrate the capabilities of tensor field networks with tasks in geometry, physics, and chemistry.
542 citations
530 citations