Non-quasiconvex subgroups of hyperbolic groups via Stallings-like techniques

Non-quasiconvex subgroups of hyperbolic groups via Stallings-like techniques

We provide a new method of constructing non-quasiconvex subgroups of hyperbolic groups by utilizing techniques inspired by Stallings' foldings. The hyperbolic groups constructed are in the natural class of right-angled Coxeter groups (RACGs for short) and can be chosen to be 2-dimensional. More...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Dani, Pallavi, Levcovitz, Ivan
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Geometric Topology
Mathematics - Group Theory
Online-Zugang:Volltext bestellen
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title
container_volume
creator Dani, Pallavi
Levcovitz, Ivan
description We provide a new method of constructing non-quasiconvex subgroups of hyperbolic groups by utilizing techniques inspired by Stallings' foldings. The hyperbolic groups constructed are in the natural class of right-angled Coxeter groups (RACGs for short) and can be chosen to be 2-dimensional. More specifically, given a non-quasiconvex subgroup of a (possibly non-hyperbolic) RACG, our construction gives a corresponding non-quasiconvex subgroup of a hyperbolic RACG. We use this to construct explicit examples of non-quasiconvex subgroups of hyperbolic RACGs including subgroups whose generators are as short as possible (length two words), finitely generated free subgroups, non-finitely presentable subgroups, and subgroups of fundamental groups of square complexes of nonpositive sectional curvature.
doi_str_mv 10.48550/arxiv.2102.11853
format Article
fullrecord <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_2102_11853</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2102_11853</sourcerecordid><originalsourceid>FETCH-LOGICAL-a673-db26a403ba3cd521e3405a3177ab019da6b26d32f779d866ae83c6018dec2feb3</originalsourceid><addsrcrecordid>eNotz8lOwzAYBGBfOKDCA3DCL-DgJV56rCo2KYIDvUe_l7QWbpzGTdS-PVB6Gmk0GulD6IHRqjZS0icYT3GuOKO8YsxIcYuaj9yTwwQlutzP4YTLZLdjnoaCc4d35yGMNqfo8LWcI-CvI6QU-20hKX4HfAxu18fDFModuukglXB_zQXavDxv1m-k-Xx9X68aAkoL4i1XUFNhQTgvOQuiphIE0xosZUsP6nfgBe-0XnqjFAQjnKLM-OB4F6xYoMf_2wunHca4h_Hc_rHaC0v8AMZCSYU</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Non-quasiconvex subgroups of hyperbolic groups via Stallings-like techniques</title><source>arXiv.org</source><creator>Dani, Pallavi ; Levcovitz, Ivan</creator><creatorcontrib>Dani, Pallavi ; Levcovitz, Ivan</creatorcontrib><description>We provide a new method of constructing non-quasiconvex subgroups of hyperbolic groups by utilizing techniques inspired by Stallings' foldings. The hyperbolic groups constructed are in the natural class of right-angled Coxeter groups (RACGs for short) and can be chosen to be 2-dimensional. More specifically, given a non-quasiconvex subgroup of a (possibly non-hyperbolic) RACG, our construction gives a corresponding non-quasiconvex subgroup of a hyperbolic RACG. We use this to construct explicit examples of non-quasiconvex subgroups of hyperbolic RACGs including subgroups whose generators are as short as possible (length two words), finitely generated free subgroups, non-finitely presentable subgroups, and subgroups of fundamental groups of square complexes of nonpositive sectional curvature.</description><identifier>DOI: 10.48550/arxiv.2102.11853</identifier><language>eng</language><subject>Mathematics - Geometric Topology ; Mathematics - Group Theory</subject><creationdate>2021-02</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2102.11853$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2102.11853$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Dani, Pallavi</creatorcontrib><creatorcontrib>Levcovitz, Ivan</creatorcontrib><title>Non-quasiconvex subgroups of hyperbolic groups via Stallings-like techniques</title><description>We provide a new method of constructing non-quasiconvex subgroups of hyperbolic groups by utilizing techniques inspired by Stallings' foldings. The hyperbolic groups constructed are in the natural class of right-angled Coxeter groups (RACGs for short) and can be chosen to be 2-dimensional. More specifically, given a non-quasiconvex subgroup of a (possibly non-hyperbolic) RACG, our construction gives a corresponding non-quasiconvex subgroup of a hyperbolic RACG. We use this to construct explicit examples of non-quasiconvex subgroups of hyperbolic RACGs including subgroups whose generators are as short as possible (length two words), finitely generated free subgroups, non-finitely presentable subgroups, and subgroups of fundamental groups of square complexes of nonpositive sectional curvature.</description><subject>Mathematics - Geometric Topology</subject><subject>Mathematics - Group Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz8lOwzAYBGBfOKDCA3DCL-DgJV56rCo2KYIDvUe_l7QWbpzGTdS-PVB6Gmk0GulD6IHRqjZS0icYT3GuOKO8YsxIcYuaj9yTwwQlutzP4YTLZLdjnoaCc4d35yGMNqfo8LWcI-CvI6QU-20hKX4HfAxu18fDFModuukglXB_zQXavDxv1m-k-Xx9X68aAkoL4i1XUFNhQTgvOQuiphIE0xosZUsP6nfgBe-0XnqjFAQjnKLM-OB4F6xYoMf_2wunHca4h_Hc_rHaC0v8AMZCSYU</recordid><startdate>20210223</startdate><enddate>20210223</enddate><creator>Dani, Pallavi</creator><creator>Levcovitz, Ivan</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20210223</creationdate><title>Non-quasiconvex subgroups of hyperbolic groups via Stallings-like techniques</title><author>Dani, Pallavi ; Levcovitz, Ivan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a673-db26a403ba3cd521e3405a3177ab019da6b26d32f779d866ae83c6018dec2feb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Mathematics - Geometric Topology</topic><topic>Mathematics - Group Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Dani, Pallavi</creatorcontrib><creatorcontrib>Levcovitz, Ivan</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Dani, Pallavi</au><au>Levcovitz, Ivan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Non-quasiconvex subgroups of hyperbolic groups via Stallings-like techniques</atitle><date>2021-02-23</date><risdate>2021</risdate><abstract>We provide a new method of constructing non-quasiconvex subgroups of hyperbolic groups by utilizing techniques inspired by Stallings' foldings. The hyperbolic groups constructed are in the natural class of right-angled Coxeter groups (RACGs for short) and can be chosen to be 2-dimensional. More specifically, given a non-quasiconvex subgroup of a (possibly non-hyperbolic) RACG, our construction gives a corresponding non-quasiconvex subgroup of a hyperbolic RACG. We use this to construct explicit examples of non-quasiconvex subgroups of hyperbolic RACGs including subgroups whose generators are as short as possible (length two words), finitely generated free subgroups, non-finitely presentable subgroups, and subgroups of fundamental groups of square complexes of nonpositive sectional curvature.</abstract><doi>10.48550/arxiv.2102.11853</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext_linktorsrc
identifier DOI: 10.48550/arxiv.2102.11853
ispartof
issn
language eng
recordid cdi_arxiv_primary_2102_11853
source arXiv.org
subjects Mathematics - Geometric Topology
Mathematics - Group Theory
title Non-quasiconvex subgroups of hyperbolic groups via Stallings-like techniques
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-04T03%3A32%3A22IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Non-quasiconvex%20subgroups%20of%20hyperbolic%20groups%20via%20Stallings-like%20techniques&rft.au=Dani,%20Pallavi&rft.date=2021-02-23&rft_id=info:doi/10.48550/arxiv.2102.11853&rft_dat=%3Carxiv_GOX%3E2102_11853%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true