## Journal of Differential Geometry

- J. Differential Geom.
- Volume 70, Number 2 (2005), 183-323.

### Non-Abelian localization for Chern-Simons theory

Chris Beasley and Edward Witten

#### Abstract

We reconsider Chern-Simons gauge theory on a Seifert manifold M (the total space of a nontrivial circle bundle over a Riemann surface Σ). When M is a Seifert manifold, Lawrence and Rozansky have shown from the exact solution of Chern-Simons theory that the partition function has a remarkably simple structure and can be rewritten entirely as a sum of local contributions from the flat connections on M. We explain how this empirical fact follows from the technique of non-abelian localization as applied to the Chern-Simons path integral. In the process, we show that the partition function of Chern-Simons theory on M admits a topological interpretation in terms of the equivariant cohomology of the moduli space of flat connections on M.

#### Article information

**Source**

J. Differential Geom., Volume 70, Number 2 (2005), 183-323.

**Dates**

First available in Project Euclid: 29 March 2006

**Permanent link to this document**

https://projecteuclid.org/euclid.jdg/1143642932

**Digital Object Identifier**

doi:10.4310/jdg/1143642932

**Mathematical Reviews number (MathSciNet)**

MR2192257

**Zentralblatt MATH identifier**

1097.58012

#### Citation

Beasley, Chris; Witten, Edward. Non-Abelian localization for Chern-Simons theory. J. Differential Geom. 70 (2005), no. 2, 183--323. doi:10.4310/jdg/1143642932. https://projecteuclid.org/euclid.jdg/1143642932