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Chifan, Ionuţ; Das, Sayan; Houdayer, Cyril; Khan, Krishnendu
American journal of mathematics, 04/2024, Volume: 146, Issue: 2Journal Article
In this article we provide the first examples of property (T) $\mathrm{II}_1$ factors $\mathcal{N}$ with trivial fundamental group, $\mathcal{F}(\mathcal{N})=1$. Our examples arise as group factors $\mathcal{N}=\mathcal{L}(G)$ where $G$ belong to two distinct families of property (T) groups previously studied in the literature: the groups introduced by Valette in Geom. Dedicata 112 (2005), 183--196 and the ones introduced recently in Anal. PDE 16 (2023), 433--476 using the Belegradek-Osin Rips construction from Groups Geom. Dyn. 2 (2008), 1--12. In particular, our results provide a continuum of explicit pairwise nonisomorphic property (T) factors.
