Work

On soficity for certain fundamental groups of graphs of groups

Year: 2026

Type: article

Abstract: In this note we study a family of graphs of groups over arbitrary base graphs where (1) all vertex groups are isomorphic to a fixed countable sofic group [Formula: see text], (2) all edge groups [Formula: see text] are such that the embeddings of [Formula: see text] into [Formula: see text] are identical everywhere. We prove soficity for this family of groups under a flexible technical hypothesis for [Formula: see text] called [Formula: see text]-sofically-separable. This proves soficity for group doubles [Formula: see text], where [Formula: see text] is an arbitrary separable subgroup and [Formula: see text] is countable and sofic. This includes arbitrary finite index group doubles of sofic groups among various other examples.

Source: Journal of Topology and Analysis

DOI: 10.1142/s1793525326500093

Authors: David Gao, Srivatsav Kunnawalkam Elayavalli, Mahan Mj

Institutions: University of California San Diego, Tata Institute of Fundamental Research

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

OpenAlex ID: W7125500580

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