arXiv 2003.052372020-03math.GT

Integrable tautness of isometries of complex hyperbolic spaces

Alessio Savini

备注：: 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

英文摘要：

Consider $n \geq 2$. 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.

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