Título:
On the geometry of positive cones in finitely generated groups
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Autor:
Alonso, Juan
Antolín, Yago
Brum, Joaquín
Rivas, Cristóbal
Antolín, Yago
Brum, Joaquín
Rivas, Cristóbal
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Tipo de documento:
Preprint
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Palabras clave:
Ordered groups
Hyperbolic groups
Nonpositively curved groups
Hyperbolic groups
Nonpositively curved groups
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Año de publicación:
2022
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Resumen:
We study the geometry of positive cones of left-invariant total orders (left-order, for short) in finitely generated groups. We introduce the Hucha property and the Prieto property for left-orderable groups. We say that a group has the Hucha property if in any left-order the corresponding positive cone is not coarsely connected, and the Prieto property if in any left-order the corresponding positive cone is coarsely connected. We show that all left-orderable free products have the Hucha property, and that the Hucha property is stable under certain free products with amalgamatation over Prieto subgroups. As an application we show that non-abelian limit groups in the sense of Z. Sela (e.g., free groups, fundamental group of hyperbolic surfaces, doubles of free groups and others) and non-abelian finitely generated subgroups of free -groups in the sense of G. Baumslag have the Hucha property. In particular, this implies that these groups have empty BNS-invariant and that they do not have finitely generated positive cones.
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Publicado también en: Journal of the London Mathematical Society, 2022, 106(4). DOI: 10.1112/jlms.12657
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arXiv
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Mathematics (Group Theory), arXiv: 10.48550/arXiv.2001.10286
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Citación:
Alonso, J, Antolín, Y, Brum, J [y otro autor]. "On the geometry of positive cones in finitely generated groups" [Preprint]. Publicado en: Mathematics (Group Theory). 2022, arXiv: 10.48550/arXiv.2001.10286, Ene 2022, pp. 1-32.
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Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
| Ficheros | Descripción | Tamaño | Formato | ||
|---|---|---|---|---|---|
| 2001.10286.pdf | Preprint | 354.79 KB | Adobe PDF |