Search results for "Equivariant map"
showing 10 items of 22 documents
On the geometric structure of the class of planar quadratic differential systems
2002
In this work we are interested in the global theory of planar quadratic differential systems and more precisely in the geometry of this whole class. We want to clarify some results and methods such as the isocline method or the role of rotation parameters. To this end, we recall how to associate a pencil of isoclines to each quadratic differential equation. We discuss the parameterization of the space of regular pencils of isoclines by the space of its multiple base points and the equivariant action of the affine group on the fibration of the space of regular quadratic differential equations over the space of regular pencils of isoclines. This fibration is principal, with a projective group…
Anomalies from nonfree action of the gauge group
1990
Abstract The question whether new anomalies appear, connected with the finite dimensional part of the gauge group isomorphic to the structure group of the theory, is investigated in a systematical way. The stability groups from the stratification of the gauge group on the space of connections lead to anomalies. The detection of these anomalies within the equivariant approach pursued here is extremely simple. For a large class of theories it is shown that no new anomalies appear.
Equivariance in topological gravity
1992
Abstract We present models of topological gravity for a variety of moduli space conditions. In four dimensions, we construct a model for self-dual gravity characterized by the moduli condition R + μν =0, and in two dimensions we treat the case of constant scalar curvature. Details are also given for both flat and Yang-Mills type moduli conditions in arbitrary dimensions. All models are based on the same fundamental multiplet which conveniently affords the construction of a complete hierarchy of observables. This approach is founded on a symmetry algebra which includes a local vector supersymmetry, in addition to a global BRST-like symmetry which is equivariant with respect to Lorentz transf…
$$O_2(\mathbb {C})$$O2(C)-Vector Bundles and Equivariant Real Circle Actions
2020
The main goal of this article is to give an expository overview of some new results on real circle actions on affine four-space and their relation to previous results on \(O_2(\mathbb {C})\)-equivariant vector bundles. In Moser-Jauslin (Infinite families of inequivalent real circle actions on affine four-space, 2019, [13]), we described infinite families of equivariant real circle actions on affine four-space. In the present note, we will describe how these examples were constructed, and some consequences of these results.
Finite type invariants of knots in homology 3-spheres with respect to null LP-surgeries
2017
We study a theory of finite type invariants for null-homologous knots in rational homology 3-spheres with respect to null Lagrangian-preserving surgeries. It is an analogue in the setting of the rational homology of the Goussarov-Rozansky theory for knots in integral homology 3-spheres. We give a partial combinatorial description of the graded space associated with our theory and determine some cases when this description is complete. For null-homologous knots in rational homology 3-spheres with a trivial Alexander polynomial, we show that the Kricker lift of the Kontsevich integral and the Lescop equivariant invariant built from integrals in configuration spaces are universal finite type i…
Equivariant cohomology, Fock space and loop groups
2006
Equivariant de Rham cohomology is extended to the infinite-dimensional setting of a loop subgroup acting on a loop group, using Hida supersymmetric Fock space for the Weil algebra and Malliavin test forms on the loop group. The Mathai–Quillen isomorphism (in the BRST formalism of Kalkman) is defined so that the equivalence of various models of the equivariant de Rham cohomology can be established.
A construction of equivariant bundles on the space of symmetric forms
2021
We construct stable vector bundles on the space of symmetric forms of degree d in n+1 variables which are equivariant for the action of SL_{n+1}(C), and admit an equivariant free resolution of length 2. For n=1, we obtain new examples of stable vector bundles of rank d-1 on P^d, which are moreover equivariant for SL_2(C). The presentation matrix of these bundles attains Westwick's upper bound for the dimension of vector spaces of matrices of constant rank and fixed size.
Tests of Independence Based on Sign and Rank Covariances
2003
In this paper three different concepts of bivariate sign and rank, namely marginal sign and rank, spatial sign and rank and affine equivariant sign and rank, are considered. The aim is to see whether these different sign and rank covariances can be used to construct tests for the hypothesis of independence. In some cases (spatial sign, affine equivariant sign and rank) an additional assumption on the symmetry of marginal distribution is needed. Limiting distributions of test statistics under the null hypothesis as well as under interesting sequences of contiguous alternatives are derived. Asymptotic relative efficiencies with respect to the regular correlation test are calculated and compar…
The asymptotic covariance matrix of the Oja median
2003
The Oja median, based on a sample of multivariate data, is an affine equivariant estimate of the centre of the distribution. It reduces to the sample median in one dimension and has several nice robustness and efficiency properties. We develop different representations of its asymptotic variance and discuss ways to estimate this quantity. We consider symmetric multivariate models and also the more narrow elliptical models. A small simulation study is included to compare finite sample results to the asymptotic formulas.
Affine Invariant Multivariate Sign and Rank Tests and Corresponding Estimates: a Review
1999
The paper reviews recent contributions to the statistical inference methods, tests and estimates, based on the generalized median of Oja. Multivariate analogues of sign and rank concepts, affine invariant one-sample and two-sample sign tests and rank tests, affine equivariant median and Hodges–Lehmann-type estimates are reviewed and discussed. Some comparisons are made to other generalizations. The theory is illustrated by two examples.