Free groups are $L^2$-subgroup rigid

Andrei Jaikin-Zapirain

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arXiv · 2403.09515

Free groups are $L^2$-subgroup rigid

Andrei Jaikin-Zapirain

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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 Antolin and Jaikin-Zapirain.

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BibTeX RIS

Andrei Jaikin-Zapirain. 2024-03-14. Free groups are $L^2$-subgroup rigid. https://arxiv.org/abs/2403.09515

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