Homology of Euclidean groups of motions made discrete and Euclidean scissors congruences (Q757913)

The authors consider the work of Dehn-Sydler-Jessen which shows that volume and Dehn invariants form a complete set of invariants for the scissors congruence problem in 3-dimensional Euclidean space. They give a proof of this result (consistent with their philosophy about scissors congruence problems) using only the homology theory of classical Lie groups made discrete. The dimension 4 version follows from that of dimension 3 by a result of Jessen. Whether the above set of invariants is complete in dimensions 5 and higher is unknown.