Journal of the European Mathematical Society· 2026Q1
Free groups are $L^{2}$-subgroup rigid
- 7citations
- Q1SCImago
- 2026year
Short summary
Free groups are proven to be $L^{2}$-subgroup rigid, a new concept introduced in this paper.
AI-generated from the title and abstract; the full text is not read.
Key points
- Introduces the novel concept of $L^{2}$-subgroup rigid groups.
- Demonstrates that free groups are $L^{2}$-subgroup rigid.
- Establishes equivalence between compressibility, inertness, strong inertness, and $L^{2}$-independence for finitely generated subgroups of free groups.
- Confirms conjectures by Dicks and Ventura, and by Antolín and Jaikin-Zapirain.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Journal of the European Mathematical Society, 2026 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics