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

Andrei Jaikin-Zapirain

doi:10.4171/jems/1831

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

Andrei Jaikin-Zapirain
Instituto de Ciencias Matemáticas, Madrid, Spain

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

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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.

Cite this article

Andrei Jaikin-Zapirain, Free groups are $L^{2}$ -subgroup rigid. J. Eur. Math. Soc. (2026), published online first

DOI 10.4171/JEMS/1831