Homological and Bloch invariants for $\mathbb{Q}$-rank one spaces and flag structures

Abstract

We use group homology to define invariants in algebraic K-theory and in an analogue of the Bloch group for $\mathbb{Q}$-rank one lattices and for some other geometric structures. We also show that the Bloch invariants of CR structures and of ag structures can be recovered by a fundamental class construction.