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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2017: 1.49

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Volume 2016, Issue 710


Quasiconvexity in relatively hyperbolic groups

Victor Gerasimov
  • Departamento de Matemática, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, Caixa Postal 702, 30161-970 Belo Horizonte, MG, Brasil
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/ Leonid Potyagailo
Published Online: 2015-07-08 | DOI: https://doi.org/10.1515/crelle-2015-0029


We study different notions of quasiconvexity for a subgroup H of a relatively hyperbolic group G. Our first result implies that relative geometric quasiconvexity is equivalent to dynamical quasiconvexity as it was conjectured by D. Osin. In the second part of the paper we prove that a subgroup H of a finitely generated relatively hyperbolic group G acts cocompactly outside its limit set if and only if it is (absolutely) quasiconvex and every infinite intersection of H with a parabolic subgroup of G has finite index in the parabolic subgroup. We also discuss relations between other properties of subgroups close to quasiconvexity.

About the article

Received: 2012-12-06

Revised: 2015-02-16

Published Online: 2015-07-08

Published in Print: 2016-01-01

Funding Source: ANR

Award identifier / Grant number: BLAN 2011 BS0101304

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2016, Issue 710, Pages 95–135, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2015-0029.

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