We study finitely generated discrete groups of hyperbolic plane isometries (including those which reverse orientation) with non-compact orbit space. A presentation by generators and relations this type group is obtained. To that end, we use the geometrical properties a fundamental region canonical form, apply Macbeath’s classical theorem on presentations simply connected spaces. Our main result...

The main purpose of this paper is computing higher algebraic K-theory of Koszul complexes over principal ideal domains. The second purpose of this paper is giving examples of comparison techniques on algebraic K-theory for Waldhausen categories without the factorization axiom.