A geometric approach to the lower algebraic K-theory of Fuchsian groups (Q1602954)

Let \(\Gamma\) be a non-elementary finitely generated Fuchsian group and \({\mathbb Z}\Gamma\) its integral group ring. By using a geometric approach, the authors of this paper give explicit formulas of the lower \(K\)-groups \(K_0 ({\mathbb Z}\Gamma)\) and \(K_1 ({\mathbb Z}\Gamma)\) and the negative \(K\)-group \(K_{-1} ({\mathbb Z}\Gamma)\).