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arXiv · 2509.19481

Relative solidity results and their applications to computations of some II$_1$ factor invariants

Juan Felipe Ariza Mejia·Dulanji Nikethani Amaraweera·Ionut Chifan·Krishnendu Khan
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Abstract

In this paper we prove that whenever $G$ is hyperbolic relative to a family of exact, ressidually finite subgroups $\{H_1, \ldots, H_n\}$, the corresponding von Neumann algebra $\mathcal L(G)$ is solid relative to the family of subalgebras $\{\mathcal L(H_1),\ldots ,\mathcal L(H_n)\}$. Building on this result and combining it with findings from geometric group theory, we construct a continuum of icc property (T) relative hyperbolic groups that give rise to pairwise non virtually isomorphic factors, each of which has trivial one-sided fundamental semigroup.

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Juan Felipe Ariza Mejia, Dulanji Nikethani Amaraweera, Ionut Chifan, Krishnendu Khan. 2025-09-23. Relative solidity results and their applications to computations of some II$_1$ factor invariants. https://arxiv.org/abs/2509.19481

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