# Lower algebraic $K$-theory of hyperbolic 3-simplex reflection groups

### Jean-François Lafont

S.U.N.Y. Binghamton, USA### Ivonne J. Ortiz

Miami University, Oxford, United States

## Abstract

A hyperbolic 3-simplex reflection group is a Coxeter group arising as a lattice in $O_{+}(3,1)$, with fundamental domain a geodesic simplex in $H_{3}$ (possibly with some ideal vertices). The classification of these groups is known, and there are exactly 9 cocompact examples, and 23 non-cocompact examples. We provide a complete computation of the lower algebraic $K$-theory of the integral group ring of all the hyperbolic 3-simplex reflection groups.

## Cite this article

Jean-François Lafont, Ivonne J. Ortiz, Lower algebraic $K$-theory of hyperbolic 3-simplex reflection groups. Comment. Math. Helv. 84 (2009), no. 2, pp. 297–337

DOI 10.4171/CMH/163