On the geometry of positive cones in finitely generated groups

Publications

>

Article

On the geometry of positive cones in finitely generated groups

Publicated to:JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES. 106 (4): 3103-3133 - 2022-12-01 106(4), DOI: 10.1112/jlms.12657

Authors: Alonso J; Antolín Y; Brum J; Rivas C

Affiliations

ICMAT, Madrid, Spain - Author

Univ Chile, Fac Ciencias, Dept Matemat, Las Palmeras 3425, Santiago 7800003, Chile - Author

Univ Complutense Madrid, Fac Ciencias Matemat, Madrid, Spain - Author

Univ La Republ, Fac Ciencias, Ctr Matemat, Montevideo 4225, Uruguay - Author

Univ Republica, Fac Ingn, Inst Matemat & Estadist Rafael Laguardia, Montevideo, Uruguay - Author

Abstract

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 (Formula presented.) -groups in the sense of G. Baumslag have the Hucha property. In particular, this implies that these groups have empty BNS-invariant (Formula presented.) and that they do not have finitely generated positive cones.

Keywords

productsspaceAutomorphisms

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES due to its progression and the good impact it has achieved in recent years, according to the agency Scopus (SJR), it has become a reference in its field. In the year of publication of the work, 2022, it was in position , thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics (Miscellaneous).

From a relative perspective, and based on the normalized impact indicator calculated from World Citations provided by WoS (ESI, Clarivate), it yields a value for the citation normalization relative to the expected citation rate of: 1.56. This indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: ESI Nov 14, 2024)

This information is reinforced by other indicators of the same type, which, although dynamic over time and dependent on the set of average global citations at the time of their calculation, consistently position the work at some point among the top 50% most cited in its field:

Weighted Average of Normalized Impact by the Scopus agency: 1.36 (source consulted: FECYT Feb 2024)
Field Citation Ratio (FCR) from Dimensions: 1.66 (source consulted: Dimensions Jun 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-06-27, the following number of citations:

WoS: 2
Scopus: 3

Impact and social visibility

Leadership analysis of institutional authors

This work has been carried out with international collaboration, specifically with researchers from: Chile; Uruguay.

Indexed in

License and use

Citations

Altmetrics

Analysis of institutional authors

Share