Work

Free groups are $L^{2}$-subgroup rigid

Year: 2026

Type: article

Abstract: In this paper, we introduce the notion of L^{2} -subgroup rigid groups and demonstrate that free groups are L^{2} -subgroup rigid. As a consequence, we establish the equivalence between compressibility, inertness, strong inertness, and L^{2} -independence for a finitely generated subgroup of a free group, confirming a conjecture by Dicks and Ventura as well as the one by Antolín and Jaikin-Zapirain.

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1831

Author: Andrei Jaikin-Zapirain

Institution: Institute of Mathematical Sciences

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Ministerio de Ciencia e Innovación

Awards: G4070000245, G5805502524