Integrable tautness of isometries of complex hyperbolic spaces

Alessio Savini

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arXiv · 2003.05237

Integrable tautness of isometries of complex hyperbolic spaces

Alessio Savini

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Abstract

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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BibTeX RIS

Alessio Savini. 2020-03-11. Integrable tautness of isometries of complex hyperbolic spaces. https://arxiv.org/abs/2003.05237

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