nLab
equivariant connection

Contents

Context

\infty-Chern-Weil theory

Differential cohomology

Representation theory

Contents

Idea

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

X BG conn equ 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.