# nLab equivariant connection

Contents

### Context

#### $\infty$-Chern-Weil theory

∞-Chern-Weil theory

∞-Chern-Simons theory

∞-Wess-Zumino-Witten theory

## Theorems

#### Differential cohomology

differential cohomology

## Application to gauge theory

#### Representation theory

representation theory

geometric representation theory

# Contents

## Idea

An equivariant connection is a connection on a bundle $\nabla$ over a space $X$ with action by a group $H$ whuch is equipped with $H$-equivariant structure, hence equivalently – in the language of higher differential geometry of smooth groupoids – an extension of a connection $\nabla \;\colon\; X \longrightarrow \mathbf{B}G_{conn}$ to a connection $\nabla_{equ}$ on the action groupoid $X//H$:

$\array{ X &\stackrel{\nabla}{\longrightarrow}& \mathbf{B}G_{conn} \\ \downarrow & \nearrow_{\mathrlap{\nabla_{equ}}} \\ X//H } \,.$

## Examples

Created on September 16, 2013 at 00:51:07. See the history of this page for a list of all contributions to it.