#### Volume 21, issue 4 (2021)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
Equivariant differential characters and Chern–Simons bundles

### Roberto Ferreiro Pérez

Algebraic & Geometric Topology 21 (2021) 1911–1940
##### Abstract

We construct Chern–Simons bundles as ${Aut}^{+}P$–equivariant $U\left(1\right)$–bundles with connection over the space of connections ${\mathsc{𝒜}}_{P}$ on a principal $G$–bundle $P\to M\phantom{\rule{-0.17em}{0ex}}$. We show that the Chern–Simons bundles are determined up to isomorphisms by their equivariant holonomy. The space of equivariant holonomies is shown to coincide with the space of equivariant differential characters of order $2$. Furthermore, we prove that the Chern–Simons theory provides, in a natural way, an equivariant differential character that determines the Chern–Simons bundles. Our construction can be applied in the case in which $M$ is a compact manifold of even dimension and for arbitrary bundle $P$ and group $G\phantom{\rule{-0.17em}{0ex}}$.

We also generalize the results to the case of the action of diffeomorphisms on the space of Riemannian metrics. In particular, in dimension $2$ we obtain a Chern–Simons bundle over the Teichmüller space.

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/agt

We have not been able to recognize your IP address 3.229.124.74 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

or by using our contact form.

##### Keywords
equivariant differential character, equivariant holonomy, Chern–Simons bundle, space of connections, space of Riemannian metrics
##### Mathematical Subject Classification 2010
Primary: 55N91, 70S15
Secondary: 53C08, 53C29, 58J28