On the bounded cohomology of Lie groups

On transfer in bounded cohomology

“…Using Lemma 4.1, it follows that already x lies in the image of H * Bb (G, M) → H * B (G, M). The following result was proved in [1] for connected Lie groups and trivial coefficients A = Z. However, in applications one is often confronted with Lie groups with finitely many connected components (virtually connected Lie groups), like GL(n, R) or O(p, q).…”

“…However, in applications one is often confronted with Lie groups with finitely many connected components (virtually connected Lie groups), like GL(n, R) or O(p, q). The transfer map allows a natural generalization of [1,Theorem 1.2] to include such groups.…”

“…In case A is equipped with a metric, one can define the Borel-bounded cohomology groups H * Bb (G, A) and study the comparison map from Borel-bounded to Borel cohomology. The case of a connected Lie group G and A = Z with trivial G-action was dealt with in [1]. The purpose of this note is to define a transfer map in the H * B and H * Bb setting, with respect to a closed subgroup H < G of finite index.…”

“…The purpose of this note is to define a transfer map in the H * B and H * Bb setting, with respect to a closed subgroup H < G of finite index. We will make use of our transfer map to extend some results proved in [1] for connected Lie groups, to cover the case of groups with finitely many connected components (virtually connected groups).…”