Stabilization of Bounded Cohomology for Classical Groups

TL;DR

This paper demonstrates that bounded cohomology stabilizes for sequences of classical Lie groups and their lattices, using a novel adaptation of Quillen's stability method applied to Stiefel complexes.

Contribution

It introduces a new criterion based on measured complexes to establish bounded cohomology stability in classical groups and lattices.

Findings

Bounded cohomology stabilizes along classical Lie group sequences.

The method adapts Quillen's stability technique to bounded cohomology.

Stiefel complexes are key tools in the stability proof.

Abstract

We show that bounded cohomology stabilizes along sequences of classical Lie groups, and along sequences of lattices in them. Our method is based on a criterion from (arXiv:2307.12808) which adapts Quillen's stability method to the setting of bounded cohomology. This criterion is then applied to a family of measured complexes, the so-called Stiefel complexes, associated to any vector space endowed with a non-degenerate sesquilinear form.