Property (T) group factors whose Jones index set equals all positive integers

Ionut Chifan; Junhwi Lim

doi:10.48550/arxiv.2511.04822

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Property (T) group factors whose Jones index set equals all positive integers

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Property (T) group factors whose Jones index set equals all positive integers

Ionut Chifan and Junhwi Lim

ArXiv.org

Cornell University

11/10/2025

DOI: 10.48550/arxiv.2511.04822

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https://doi.org/10.48550/arxiv.2511.04822View

Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

Using a mélange of techniques at the rich intersection of deformation/rigidity theory, finite index subfactor theory, and geometric group theory, we prove the existence of a continuum of property (T) factors that are pairwise non-stably isomorphic and whose Jones index sets consist of all positive integers. These factors are realized as group von Neumann algebras associated with property (T) generalized wreath-like product groups introduced in [CIOS23b], where is abelian, is a non-parabolic subgroup of a relatively hyperbolic group with residually finite peripheral structure, and is a faithful action with infinite orbits. Integer index subfactors of are constructed from extensions of . This result advances an open question of P. de la Harpe [dlH95].

Mathematics - Group Theory

Mathematics - Operator Algebras

Details

Title: Subtitle: Property (T) group factors whose Jones index set equals all positive integers
Creators: Ionut Chifan
Junhwi Lim - Vanderbilt University
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2511.04822
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 11/10/2025
Academic Unit: Mathematics
Record Identifier: 9985026457402771

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