Recent updates on homological invariants of bieberbach groups

Abstract

Homological invariants or homological functors of groups have their roots in algebraic K-theory and homotopy theory. They were first used in algebraic topology, but are common in many areas of mathematics. The homological invariants are also used in group cohomology to classify abelian group extensions. Researches on homological invariants have grown intensively over the years. In this paper, recent updates of the homological invariants of Bieberbach groups with certain point groups will be presented. Furthermore, some of the homological invariants of a Bieberbach group of dimension six with quaternion point group of order eight are computed.