Parametrization of the moduli space of flat \(\text{SL}(2,\mathbb{R})\) connections on the torus (Q1609424)

The main result concerns the moduli space of flat \(\text{SL}(2,\mathbb{R})\)-connections on the torus. The main tool is identification of this space with \(\Hom (\mathbb{Z}^2,G)/G\) where \(G= \text{SL}(2,\mathbb{R})\) acts by conjugation and \(\mathbb{Z}^2\) is a free abelian group of rank 2. Moreover the authors parametrize it using spectral properties of certain \(2\times 2\)-matrices. In particular, a Hausdorff topology based on the above is proposed.