Examples of property (T) II₁ factors with trivial fundamental group

2020/03/19 by Ionuţ Chifan, Ionut Chifan, Chifan, Ionut +6 · 2 citations
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Operator Algebras (math.OA) #math.GR #math.OA

paper · pdf · doi:10.48550/arxiv.2003.08857

New classes of property (T) factors with trivial fundamental groups added. New co-author added

openalex publication_date 2020/03/19 · arxiv created 2020/03/28 · arxiv updated 2020/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

In this article we provide the first examples of property (T) \rm II₁ 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 \citeVa04 and the ones introduced recently in \citeCDK19 using the Belegradek-Osin Rips construction from \citeBO06. In particular, our results provide a continuum of explicit pairwise non-isomorphic property (T) factors.

Cited by

• Property (T) group factors whose Jones index set equals all positive integers
• Relative solidity results and their applications to computations of some II₁ factor invariants

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