Seppälä, Mika; Sorvali, Tuomas Traces of commutators of Möbius transformations. (English) Zbl 0898.30037 Math. Scand. 68, No. 1, 53-58 (1991). The question of lifting subgroups of \(\text{PSL}(2,\mathbb{R})\) to \(\text{SL}(2,\mathbb{R})\) has an interesting history. In this connection see papers by the reviewer in [Differential geometry and complex analysis, Vol. dedic. H. E. Rauch, 181-193 (1985; Zbl 0571.30037)] and by M. Culler [Adv. Math. 59, No. 1, 64-70 (1986; Zbl 0582.57001)]. The authors reprove by elementary methods, that a Fuchsian group uniforming a compact surface of genus \(>1\) lifts. The basic fact established in this paper is that the trace of the commutator of a pair of hyperbolic Möbius transformations with intersecting axes is negative. Reviewer: I.Kra (MR 92k:20093) Cited in 5 Documents MSC: 30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization) Citations:Zbl 0571.30037; Zbl 0582.57001 PDFBibTeX XMLCite \textit{M. Seppälä} and \textit{T. Sorvali}, Math. Scand. 68, No. 1, 53--58 (1991; Zbl 0898.30037) Full Text: DOI EuDML