Berkove, Ethan; Juan-Pineda, Daniel; Pearson, Kimberly The lower algebraic K-theory of Fuchsian groups. (English) Zbl 0986.19001 Comment. Math. Helv. 76, No. 2, 339-352 (2001). A Fuchsian group is a discrete subgroup of \(\text{PSL}_2 ({\mathbb R})\) or a conjugate of such a group in \(\text{PSL}_2 ({\mathbb C})\). Since \(\text{PSL}_2 ({\mathbb R})\) can be identified with the orientation-preserving isometries of the hyperbolic plane \({\mathbb H}^2\), the Fuchsian groups act in a natural way on \({\mathbb H}^2\). F. T. Farrell and L. E. Jones [J. Am. Math. Soc. 6, No. 2, 249-297 (1993; Zbl 0798.57018)] proved that there is a significant simplification in calculating the lower algebraic \(K\)-theory of discrete cocompact subgroups of virtually connected Lie groups and their subgroups. In this paper, the authors show that a further reduction can be made, and use spectral sequences to calculate the lower algebraic \(K\)-groups of the integral group ring \({\mathbb Z} \Gamma\), where \(\Gamma\) is a cocompact Fuchsian group. Reviewer: Li Fu-an (Beijing) Cited in 1 ReviewCited in 3 Documents MSC: 19A31 \(K_0\) of group rings and orders 19D35 Negative \(K\)-theory, NK and Nil 19B28 \(K_1\) of group rings and orders Keywords:Fuchsian groups; Kleinian groups Citations:Zbl 0798.57018 PDFBibTeX XMLCite \textit{E. Berkove} et al., Comment. Math. Helv. 76, No. 2, 339--352 (2001; Zbl 0986.19001) Full Text: DOI