Homology of O(n) and O1(1,n) made discrete: An application of edgewise subdivision Original Research Article

The group of isometrics of hyperbolic n-space contains the orthogonal group O(n) as a subgroup. We prove that this inclusion induces a stable isomorphism of discrete group homology. The unstable version of this result implies in particular that the scissors congruence group image in spherical 3-space is a rational vectorspace.