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

doi:10.48550/arxiv.2509.19481

Back

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

Preprint

Open access

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

Juan Felipe Ariza Mejia, Dulanji Nikethani Amaraweera, Ionut Chifan and Krishnendu Khan

ArXiv.org

Cornell University

09/23/2025

DOI: 10.48550/arxiv.2509.19481

Files and links (1)

url

https://doi.org/10.48550/arxiv.2509.19481View

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

In this paper we prove that whenever G is hyperbolic relative to a family of exact, ressidually finite subgroups {H1,...,Hn}, the corresponding von Neumann algebra L(G) is solid relative to the family of subalgebras {L(H1),...,L(Hn)}. 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.

Mathematics - Operator Algebras

Details

Title: Subtitle: Relative solidity results and their applications to computations of some II$_1$ factor invariants
Creators: Juan Felipe Ariza Mejia
Dulanji Nikethani Amaraweera
Ionut Chifan
Krishnendu Khan
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2509.19481
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 09/23/2025
Academic Unit: Mathematics
Record Identifier: 9984964742102771

Metrics

3 Record Views