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arXiv · 2404.00433

Property $\mathrm{(TTT)}$ and the Cowling--Haagerup constant

Ignacio Vergara
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Abstract

We show that Property $\mathrm{(TTT)}$ is an obstruction to weak amenability with Cowling--Haagerup constant $1$. More precisely, if $G$ is a countable group and $H$ is an infinite subgroup of $G$ such that the pair $(G,H)$ has relative Property $\mathrm{(TTT)}$, then the weak Haagerup constant $\boldsymbol\Lambda_{\mathrm{WH}}(G)$ is strictly greater than $1$. We apply this result to some semidirect products and lattices in higher rank algebraic groups.

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Ignacio Vergara. 2024-03-30. Property $\mathrm{(TTT)}$ and the Cowling--Haagerup constant. https://doi.org/10.1007/s11785-024-01613-2

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