Homological and Bloch invariants for Q-rank one spaces and flag structures

TL;DR

This paper introduces new invariants derived from group homology for Q-rank one lattices and geometric structures, connecting algebraic K-theory with geometric invariants like Bloch invariants.

Contribution

It defines novel invariants in algebraic K-theory and Bloch group analogues for Q-rank one spaces, linking them to fundamental class constructions.

Findings

Bloch invariants can be recovered via fundamental class construction.

Group homology provides a framework for defining these invariants.

The invariants apply to CR structures and flag structures.

Abstract

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