Integrable tautness of isometries of complex hyperbolic spaces

Abstract

Consider $n\ge 2$. In this paper we prove that the group $\text{PU}(n,1)$ is $1$-taut. This result concludes the study of $1$-tautness of rank-one Lie groups of non-compact type. Additionally the tautness property implies a classification of finitely generated groups which are ${\text{L}}^1$-measure equivalent to lattices of $\text{PU}(n,1)$. More precisely, we show that ${\text{L}}^1$-measure equivalent groups must be extensions of lattices of $\text{PU}(n,1)$ by a finite group.

There is an issue in the proof of Lemma 3.7: evaluation of the involved classes gives back the same values for the coinvariants and not necessarily for the coefficients themselves. At the moment I do not see how to fix it. The lemma is needed in the proof of the main Theorem

References in corpus (1)

• Superrigidity of maximal measurable cocycles of complex hyperbolic lattices

Cited by in corpus (2)

• Multiplicative constants and maximal measurable cocycles in bounded cohomology
• Equivariant maps for measurable cocycles with values into higher rank Lie groups