A quotient stack is defined as follows. Let G be an affine smooth group scheme over a scheme S and X an S-scheme on which G acts.Let the quotient stack [/] be the category over the …

In geometry and topology, given a group G (which may be a topological or Lie group), an equivariant bundle is a fiber bundle such that the total space and the base space are both G …

Aug 4, 2020 · Abstract: We compare two notions of $G$-fiber bundles and $G$-principal bundles in the literature, with an aim to clarify early results in equivariant bundle theory that are needed …

In mathematics, and especially differential geometry and gauge theory, a connection is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points.

Sep 1, 2021 · Usually, "being covariantly constant" is used for sections $s$ in vector bundles $E$ which carry a covariant derivative $\nabla$, and then in the obvious way $\nabla s=0$. The …

We consider –equivariant principal G–bundles over proper –CW–complexes with a prescribed family of local representations. We construct and analyze their classifying spaces for locally …

Then, we prove an equivalence between the groupoid fibration of A-equivariant G-bundles on ?’ and quasi-parabolic G-bundles on an s-pointed curve ? = ?’/A consisting of the A-ramification …

Principal bundles have important applications in topology and differential geometry and mathematical gauge theory. They have also found application in physics where they form part …

As indicated above, we seek a functor K(−)(−) : RTopop → Ring, called equivariant K-theory, which fits into the following diagram. K(X), G = ∗. In fact, when restricting to the category of …

3 days ago · We study holomorphic vector bundles equipped with a compatible action of vector field by Lie derivatives.We will show that the dependence of the Lie derivative on a vector field …

In mathematics, equivariant topology is the study of topological spaces that possess certain symmetries. In studying topological spaces, one often considers continuous maps f : X → Y …

equivalence between the category of real vector bundles over X as space and the category of real vector bundles over X as real space. The equivalence maps a vector bundle E to E b R C. As a result, KRpXq KOpXq. We are now going to extend KR …

We show that every G-equivariant vector bundle on an affine toric scheme over R with G-action is equivariantly extended from Spec.R for several cases of R.

In mathematics, equivariant cohomology (or Borel cohomology) is a cohomology theory from algebraic topology which applies to topological spaces with a group action. It can be viewed as …