[2206.06749] Growth of quasi-convex subgroups in groups with a constricting element Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Group Theory arXiv:2206.06749 (math) [Submitted on 14 Jun 2022 ( v1 ), last revised 24 Apr 2026 (this version, v2)] Title: Growth of quasi-convex subgroups in groups with a constricting element Authors: Xabier Legaspi View a PDF of the paper titled Growth of quasi-convex subgroups in groups with a constricting element, by Xabier Legaspi View PDF HTML (experimental) Abstract: Given a group G acting on a geodesic metric space, we consider a preferred collection of paths of the space -- a path system -- and study the spectrum of relative exponential growth rates and quotient exponential growth rates of the infinite index subgroups of G which are quasi-convex with respect to this path system. If G contains a constricting element with respect to the same path system, we are able to determine when the first kind of growth rates are strictly smaller than the growth rate of G, and when the second kind of growth rates coincide with the growth rate of G. Examples of applications include relatively hyperbolic groups, CAT(0) groups and hierarchically hyperbolic groups containing a Morse element. Comments: 40 pages, 2 figures, author accepted manuscript Subjects: Group Theory (math.GR) ; Geometric Topology (math.GT); Metric Geometry (math.MG) MSC classes: 20F06, 20F65, 20F67, 20F69 Cite as: arXiv:2206.06749 [math.GR] (or arXiv:2206.06749v2 [math.GR] for this version) https://doi.org/10.48550/arXiv.2206.06749 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Groups Geom. Dyn. 18 (2024), no. 4, pp. 1469-1505 Related DOI : https://doi.org/10.4171/ggd/788 Focus to learn more DOI(s) linking to related resources Submission history From: Xabier Legaspi [ view email ] [v1] Tue, 14 Jun 2022 10:50:12 UTC (58 KB) [v2] Fri, 24 Apr 2026 21:54:41 UTC (84 KB) Full-text links: Access Paper: View a PDF of the paper titled Growth of quasi-convex subgroups in groups with a constricting element, by Xabier Legaspi View PDF HTML (experimental) TeX Source view license Current browse context: math.GR < prev | next > new | recent | 2022-06 Change to browse by: math math.GT math.MG References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from