https://m2.mtmt.hu/ eng 2026-05-01 02:54 JournalArticle 2123049 ADMIN_APPROVED true Cited By :29 Export Date: 8 February 2020 Correspondence Address: Abért, M.; Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15, H-1053 Budapest, Hungary; email: abert@renyi.hu Funding details: Engineering and Physical Sciences Research Council, EPSRC, EP/H045112/1 Cited By :35 Export Date: 22 May 2021 Correspondence Address: Abért, M.; Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15, H-1053 Budapest, Hungary; email: abert@renyi.hu Funding details: Engineering and Physical Sciences Research Council, EPSRC, EP/H045112/1 0 2015-05-12T14:03:17.000+0000 false 2123049 2026-02-24T00:41:42.224+0000 2023-09-19T12:56:50.966+0000 2012-11-21T10:16:04.000+0000 true 10011747 Abért Miklós /api/author/10011747 Author Miklós Abért (Csoportelmélet) true 10011747 2024-06-28T07:13:50.790+0000 2012-11-21T11:15:08.000+0000 true 10015168 Szakonyi Erzsebet /api/admin/10015168 Admin Erzsebet Szakonyi (RAMKI admin 4) true 10015168 true false true 24 24 /api/publicationtype/24 PublicationType Journal Article 1 true 24 JournalArticle true 10000059 Article true 24 24 /api/publicationtype/24 PublicationType Journal Article 1 true 24 JournalArticle /api/subtype/10000059 Szakcikk SubType Article (Journal Article) 101 true 10000059 true 1 /api/category/1 Category Scientific true 1 Abért, M true true /api/journal/10001247 REVIEWED JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY 1435-9855 1435-9863 true false 10001247 false 10001247 true 1435-9855 1435-9863 Journal FOREIGN 14 5 1657 1677 1657 21 2012 We study the growth of the rank of subgroups of finite index in residually finite groups, by relating it to the notion of cost. As a by-product, we show that the 'rank vs. Heegaard genus' conjecture on hyperbolic 3-manifolds is incompatible with the 'fixed price problem' in topological dynamics. © European Mathematical Society 2012. 2012 703443 true true true false true false GREEN 2026-02-24 true http://real.mtak.hu/121709 90 0 70 58 5 66 63 59 58 64 64 52 52 76 14 0 90 76 70 58 0 4 4 Folyóiratcikk Journal Article 24 58 Könyvrészlet Chapter in Book 25 7 Könyv Book 23 5 Egyéb konferenciaközlemény Conference paper 31 0 Egyéb konferenciakötet Conference proceedings 32 0 Oltalmi formák Protection forms 26 0 Disszertáció Thesis 28 8 Egyéb Miscellaneous 29 12 Alkotás Achievement 22 0 Kutatási adat Research data 33 0 Folyóiratcikk Journal Article 24 0 0 0 Könyvrészlet Chapter in Book 25 0 0 0 Könyv Book 23 0 0 0 Egyéb konferenciaközlemény Conference paper 31 0 0 0 Egyéb konferenciakötet Conference proceedings 32 0 0 0 Oltalmi formák Protection forms 26 0 0 0 Disszertáció Thesis 28 0 0 0 Egyéb Miscellaneous 29 0 0 0 Alkotás Achievement 22 0 0 0 Kutatási adat Research data 33 0 0 0 2006 0 1 1 1 1 2007 0 0 0 0 0 2008 0 0 0 0 0 2009 0 2 2 2 2 2010 0 3 3 3 3 2011 0 5 4 5 4 2012 0 3 2 3 2 2013 0 8 7 8 7 2014 0 7 5 7 5 2015 0 6 5 6 5 2016 0 8 6 8 6 2017 0 6 5 6 5 2018 0 7 7 7 7 2019 0 12 11 12 11 2020 0 7 5 7 5 2021 0 1 1 1 1 2022 0 3 2 3 2 2023 0 2 1 2 1 2024 0 2 2 2 2 2025 0 6 6 6 6 D1 true 10011747 false false false 2012-11-21T11:15:08.000+0000 2012-11-21T11:09:37.000+0000 Algebra (HRN RAMKI) 1 8 1 2 0 true Language 10002 /api/language/10002 English Angol English true 2 true PersonAuthorship 3295697 /api/authorship/3295697 Abért, M [Abért, Miklós (Csoportelmélet), author] Algebra 1 0.5 true false Author 10011747 /api/author/10011747 Miklós Abért (Csoportelmélet) Abért Miklós true 10011747 true Abért M true false false AuthorshipType 1 /api/authorshiptype/1 Author 0 true 0 true false 16028439 true PersonAuthorship 3295698 /api/authorship/3295698 Nikolov, N 2 0.5 false true Nikolov N true false false AuthorshipType 1 /api/authorshiptype/1 Author 0 true 0 true false 16028438 true PublicationIdentifier 593145 /api/publicationidentifier/593145 DOI: 10.4171/JEMS/344 PlainSource 6 /api/publicationsource/6 DOI PublicationSourceType 10001 /api/publicationsourcetype/10001 DOI true true true DOI DOI https://doi.org/@@@ true true 6 true false IDENTICAL 10.4171/JEMS/344 https://doi.org/10.4171/JEMS/344 false 368674 true PublicationIdentifier 593143 /api/publicationidentifier/593143 WoS: 000308126300011 PlainSource 1 /api/publicationsource/1 WoS PublicationSourceType 10003 /api/publicationsourcetype/10003 Indexelő adatbázis false true true WoS WoS https://www.webofscience.com/wos/woscc/full-record/@@@ true true 1 true false IDENTICAL 000308126300011 https://www.webofscience.com/wos/woscc/full-record/000308126300011 false 951134 true PublicationIdentifier 18483712 /api/publicationidentifier/18483712 REAL: 121709 SwordSource 36 /api/publicationsource/36 REAL PublicationSourceType 10007 /api/publicationsourcetype/10007 Repozitórium true true true REAL REAL http://real.mtak.hu/@@@ true true 36 true GREEN true 121709 http://real.mtak.hu/121709 false true PublicationIdentifier 593144 /api/publicationidentifier/593144 Scopus: 84866034563 PlainSource 3 /api/publicationsource/3 Scopus PublicationSourceType 10003 /api/publicationsourcetype/10003 Indexelő adatbázis false true true Scopus Scopus http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-@@@ true true 3 true false IDENTICAL 84866034563 http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84866034563 false 368675 true PublicationIdentifier 15030490 /api/publicationidentifier/15030490 Teljes dokumentum: http://people.maths.ox.ac.uk/grabowski/files/Abert,%20Nikolov%20-%20rank%20gradient%20and%203-manifolds.pdf PlainSource 39 /api/publicationsource/39 Full text PublicationSourceType 10006 /api/publicationsourcetype/10006 Link true true true Teljes dokumentum Full text @@@ true true 39 true NO http://people.maths.ox.ac.uk/grabowski/files/Abert,%20Nikolov%20-%20rank%20gradient%20and%203-manifolds.pdf http://people.maths.ox.ac.uk/grabowski/files/Abert,%20Nikolov%20-%20rank%20gradient%20and%203-manifolds.pdf false 9045523 true PublicationIdentifier 593146 /api/publicationidentifier/593146 Mathematical Reviews: MR2966663 PlainSource 7 /api/publicationsource/7 Mathematical Reviews PublicationSourceType 10003 /api/publicationsourcetype/10003 Indexelő adatbázis false true true Mathematical Reviews Mathematical Reviews https://mathscinet.ams.org/mathscinet-getitem?mr=@@@ true true 7 true false NO MR2966663 https://mathscinet.ams.org/mathscinet-getitem?mr=MR2966663 false 1137522 true PublicationIdentifier 15016377 /api/publicationidentifier/15016377 arXiv: math/0701361 PlainSource 37 /api/publicationsource/37 arXiv PublicationSourceType 10007 /api/publicationsourcetype/10007 Repozitórium true true true arXiv http://arxiv.org/abs/@@@ true true 37 true NO math/0701361 http://arxiv.org/abs/math/0701361 false 9120431 true Classification 10006 /api/classification/10006 Algebra true true Classification 10004 /api/classification/10004 Pure mathematics, Applied mathematics true true Classification 10003 /api/classification/10003 Mathematics true true Classification 10002 /api/classification/10002 NATURAL SCIENCES true true Classification 10001 /api/classification/10001 Science true true SjrRating 5659605 /api/sjrrating/5659605 sjr:D1 (2012) Scopus - Applied Mathematics JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY 1435-9855 1435-9863 6 0.1 journal RatingType 10002 /api/ratingtype/10002 sjr sjr true true ClassificationExternal 2604 /api/classificationexternal/2604 Scopus - Applied Mathematics true 2604 true D1 DIRECT true 5659605 true Reference 1573006 /api/reference/1573006 1. Abért, M., On Chains of Subgroups in Residually Finite Groups, , Preprint 1 false true Reference 1573007 /api/reference/1573007 2. Abért, M., Jaikin-Zapirain, A., Nikolov, N., The rank gradient from a combinatorial viewpoint (2011) Groups Geom. Dynam., 5, pp. 213-230. , Zbl pre06010056 MR 2782170 2 false true Reference 1573008 /api/reference/1573008 3. Abert, M., Virag, B., Dimension and randomness in groups acting on rooted trees (2005) Journal of the American Mathematical Society, 18 (1), pp. 157-192. , PII S0894034704004679, DOI: 10.1090/S0894-0347-04-00467-9, 3 10.1090/S0894-0347-04-00467-9, false true Reference 1573009 /api/reference/1573009 4. Abért, M., Weiss, B., Bernoulli Actions Are Weakly Contained in Any Free Action, , Ergodic Theory Dynam. Systems, to appear 4 false true Reference 1573010 /api/reference/1573010 5. Agol, I., Criteria for virtual fibering (2008) J. Topology, 1, pp. 269-284. , Zbl 1148.57023 MR 2399130 5 false true Reference 1573011 /api/reference/1573011 6. Bergeron, N., Gaboriau, D., Asymptotique des nombres de Betti, invariants l 2 et laminations (2004) Commentarii Mathematici Helvetici, 79 (2), pp. 362-395., DOI: 10.1007/s00014-003-0798-1 6 10.1007/s00014-003-0798-1 false true Reference 1573012 /api/reference/1573012 7. Boileau, M., Zieschang, H., Heegaard genus of closed orientable Seifert 3-manifolds (1984) Invent. Math., 76, pp. 455-468. , Zbl 0538.57004 MR 0746538 7 false true Reference 1573013 /api/reference/1573013 8. Dooley, A.H., Ya., G.V., The Cost of An Equivalence Relation Is Determined by the Cost of A Finite Index Subrelation, , Preprint 8 false true Reference 1573014 /api/reference/1573014 9. Farber, M., Geometry of growth: Approximation theorems for L 2 invariants (1998) Mathematische Annalen, 311 (2), pp. 335-375 9 false true Reference 1573015 /api/reference/1573015 10. Gaboriau, D., Invariants l2 de relations d'équivalence et de groupes (2002) Publ. Math. Inst. Hautes Études Sci., 95, pp. 93-150. , Zbl 1022.37002 MR 1953191 10 false true Reference 1573016 /api/reference/1573016 11. Gaboriau, D., Co○ut des relations d'équivalence et des groupes (2000) Invent. Math., 139, pp. 41-98. , Zbl 0939.28012 MR 1728876 11 false true Reference 1573017 /api/reference/1573017 12. Grigorchuk, R.I., Nekrashevich, V.V., Suschanskii, V.I., Automata, dynamical systems, and groups (2000) Proc. Steklov Inst. Math., 231, pp. 128-203. , Zbl 1155.37311 MR 1841755 12 false true Reference 1573018 /api/reference/1573018 13. Gruschko, I., Ü ber die Basen eines freien Produktes von Gruppen (1940) Rec. Math. [Mat. Sbornik] N.S., 8 (50), pp. 169-182. , (in Russian; German summary) Zbl 0023.30102 MR 0003412 13 false true Reference 1573019 /api/reference/1573019 14. Kechris, A.S., Weak containment in the space of actions of a free group (2012) Israel J. Math., 189, pp. 461-507. , MR 2931406 14 false true Reference 1573020 /api/reference/1573020 15. Kechris, A.S., Miller, B., Topics in orbit equivalence (2004) Lecture Notes in Math., 1852. , Springer, Berlin, Zbl 1058.37003 MR 2095154 15 false true Reference 1573021 /api/reference/1573021 16. Lackenby, M., Heegaard splittings, the virtually Haken conjecture and Property (γ) (2006) Inventiones Mathematicae, 164 (2), pp. 317-359., DOI: 10.1007/s00222-005-0480-x 16 10.1007/s00222-005-0480-x false true Reference 1573022 /api/reference/1573022 17. Lackenby, M., Expanders, rank and graphs of groups (2005) Israel Journal of Mathematics, 146, pp. 357-370 17 false true Reference 1573023 /api/reference/1573023 18. Levitt, G., On the cost of generating an equivalence relation (1995) Ergodic Theory Dynam. Systems, 15, pp. 1173-1181. , Zbl 0843.28010 MR 1366313 18 false true Reference 1573024 /api/reference/1573024 19. Lubotzky, A., Eigenvalues of the Laplacian, the first Betti number and the congruence subgroup problem (1996) Ann. of Math., 144 (2), pp. 441-452. , Zbl 0885.11037 MR 1418904 19 false true Reference 1573025 /api/reference/1573025 20. Lück, W., L2-invariants: Theory and applications to geometry and K-theory (2002) Ergeb. Math. Grenzgeb., 44. , Springer, Berlin, Zbl 1009.55001 MR 1926649 20 false true Reference 1573026 /api/reference/1573026 21. Neumann, B.H., On the number of generators of a free product (1943) J. London Math. Soc., 18, pp. 12-20. , Zbl 0028.33901 MR 0008809 21 false true Reference 1573027 /api/reference/1573027 22. Osin, D., Rank gradient and torsion groups (2011) Bull. London Math. Soc., 43, pp. 10-16. , Zbl pre05853304 MR 2765544 22 false true Reference 1573028 /api/reference/1573028 23. Reid, A., A non-Haken hyperbolic 3-manifold covered by a surface bundle (1995) Pacific J. Math., 167, pp. 163-182. , Zbl 0817.57014 MR 1318168 23 false true Reference 1573029 /api/reference/1573029 24. Sarnak, P., Xue, X.X., Bounds for multiplicities of automorphic representations (1991) Duke Math. J., 64, pp. 207-227. , Zbl 0741.22010 MR 1131400 24 false true Reference 1573030 /api/reference/1573030 25. Schlage-Puchta, J.-C., A p-group with positive rank gradient (2012) J. Group Theory, 15, pp. 261-270 25 false true Reference 1573031 /api/reference/1573031 26. Schultens, J., Weidman, R., On the geometric and the algebraic rank of graph manifolds (2007) Pacific J. Math., 231, pp. 481-510. , Zbl 1171.57020 MR 2346507 26 false true Reference 1573032 /api/reference/1573032 27. Shalen, P., Hyperbolic volume, Heegaard genus and ranks of groups (2007) Workshop on Heegaard Splittings (Haifa, Israel, 2005), Geom. Topol. Monogr., 12, pp. 335-349. , Geom Topol Publ Coventry, Zbl 1140.57009 MR 2408254 27 false true Reference 1573033 /api/reference/1573033 28. Sharma, R., Venkataramana, T.N., Generations of arithmetic groups (2005) Geom. Dedicata, 114, pp. 103-146. , Zbl 1112.20044 MR 2174097 28 false true Reference 1573034 /api/reference/1573034 29. Stillwell, J., (1993) Classical Topology and Combinatorial Group Theory, , 2nd ed., Springer, Zbl 0774.57002 MR 1211642 29 false true Reference 1573035 /api/reference/1573035 30. Stuck, G., Zimmer, R.J., Stabilizers for ergodic actions of higher rank semisimple groups (1994) Ann. of Math., 139 (2), pp. 723-747. , Zbl 0836.22018 MR 1283875 30 false true Reference 1573036 /api/reference/1573036 31. Thurston, W., (1978) Geometry and Topology of 3-Manifolds, , Lecture Notes Princeton Univ 31 false true Reference 1573037 /api/reference/1573037 32. Waldhausen, F., Some problems on 3-manifolds (1978) Proc. Sympos. Pure Math., 32 (PART 2), pp. 313-322. , Amer. Math. Soc., Zbl 0397.57007 MR 0520549 32 false true /api/publication/2123049 Abért M et al. Rank gradient, cost of groups and the rank versus Heegaard genus problem. (2012) JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY 1435-9855 1435-9863 14 5 1657-1677<div class="JournalArticle Publication long-list"> <div class="authors"> <img title="Forrásközlemény" style="float: left" src="/frontend/resources/grid/publication-core-icon.png"> <img title="Idézőközlemény" style="float: left" src="/frontend/resources/grid/publication-citation-icon.png"> <div class="autype autype0"> <span class="author-name" mtid="10011747"><a href="/gui2/?type=authors&mode=browse&sel=10011747" target="_blank">Abért M (<span class="authorship-author-name">Abért Miklós</span> <span class="authorAux-mtmt"> Csoportelmélet</span>) </a> </span> <span class="author-affil"><span title="Alfréd Rényi Institute of Mathematics">RAMKI</span>/Algebra</span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" >Nikolov N </span> </div> </div> <div class="title"><a href="/gui2/?mode=browse&params=publication;2123049" target="_blank">Rank gradient, cost of groups and the rank versus Heegaard genus problem</a></div> <div> <span class="journal-title">JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY</span> <span class="journal-issn">(<a target="_blank" href="https://portal.issn.org/resource/ISSN/1435-9855">1435-9855</a> <a target="_blank" href="https://portal.issn.org/resource/ISSN/1435-9863">1435-9863</a>)</span>: <span class="journal-volume">14</span> <span class="journal-issue">5</span> <span class="page"> pp 1657-1677 </span> <span class="year">(2012)</span> </div> <div class="pub-footer"> <span class="language" xmlns="http://www.w3.org/1999/html">Language: English | </span> <span class="identifiers"> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="10.4171/JEMS/344" target="_blank" href="https://doi.org/10.4171/JEMS/344"> DOI </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="000308126300011" target="_blank" href="https://www.webofscience.com/wos/woscc/full-record/000308126300011"> WoS </a> </span> <span class="id identifier oa_GREEN" title=" Green "> <a style="color:black" title="121709" target="_blank" href="http://real.mtak.hu/121709"> REAL </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="84866034563" target="_blank" href="http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84866034563"> Scopus </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="http://people.maths.ox.ac.uk/grabowski/files/Abert,%20Nikolov%20-%20rank%20gradient%20and%203-manifolds.pdf" target="_blank" href="http://people.maths.ox.ac.uk/grabowski/files/Abert,%20Nikolov%20-%20rank%20gradient%20and%203-manifolds.pdf"> Full text </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="MR2966663" target="_blank" href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR2966663"> Mathematical Reviews </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="math/0701361" target="_blank" href="http://arxiv.org/abs/math/0701361"> arXiv </a> </span> </span> <OnlyViewableByAuthor><div class="ratings"> <div class="journal-subject">Journal subject: Scopus - Applied Mathematics&nbsp;&nbsp;&nbsp;Rank:&nbsp;D1</div> <div class="journal-subject">Journal subject: Scopus - Mathematics (miscellaneous)&nbsp;&nbsp;&nbsp;Rank:&nbsp;D1</div> </div></OnlyViewableByAuthor> <div class="publication-citation" style="margin-left: 0.5cm;"> <span title="" class="citingPub-count">Citing papers: 90</span> | Independent citation: 76 | Self citation: 14 | Unknown citation: 0 | Number of citations in WoS: 59 | Number of citations in Scopus:&nbsp;58 | WoS/Scopus assigned:&nbsp;64 | Number of citations with DOI:&nbsp;63 </div> <div class="publication-citation"> <a target="_blank" href="/api/publication?cond=citations.related;eq;2123049&sort=publishedYear,desc&sort=title"> Number of cited publications: 4 </a> </div> <div class="mtid"><span class="long-pub-mtid">Publication: 2123049</span> | <span class="status-data status-ADMIN_APPROVED"> Admin approved </span> <span class="oldId">Old id: 2123049</span> | Core Citing | <span class="type-subtype">Journal Article ( Article ) </span> | <span class="pub-category">Scientific</span> | <span class="publication-sourceOfData">Scopus</span> </div> <div class="lastModified">Last Modified: 2023.09.19. 14:56 Gusztáv Ladányi (MTMT API user, admin) </div> <pre class="comment" style="margin-top: 0; margin-bottom: 0;"><u>Comments</u>: Cited By :29 Export Date: 8 February 2020 Correspondence Address: Abért, M.; Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15, H-1053 Budapest, Hungary; email: abert@renyi.hu Funding details: Engineering and Physical Sciences Research Council, EPSRC, EP/H045112/1 Cited By :35 Export Date:...</pre> </div></div>