https://m2.mtmt.hu/ hun 2026-05-02 01:06 JournalArticle 33653831 ADMIN_APPROVED true Export Date: 13 September 2023 Funding details: National Science Foundation, NSF, DMS-1611851, DMS-1654114 Funding details: European Research Council, ERC, 648017 Funding details: Israel Science Foundation, ISF, 2095/15 Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, K109684 Funding text 1: Abert’s work was partially supported by European Research Council (ERC) Consolidator Grant 648017 and National Research, Development and Innovation Office (NKFIH) grant K109684. Bergeron’s work was partially supported by National Science Foundation (NSF) grant DMS-1611851 and CAREER Award DMS-1654114. Gelander’s work was partially supported by Israel Science Foundation (ISF) Moked grant 2095/15. 0 false 2026-02-24T00:41:28.767+0000 2024-01-15T15:18:51.036+0000 2023-02-22T15:41:25.783+0000 true 10015168 Szakonyi Erzsebet /api/admin/10015168 Admin true 10015168 2025-02-13T13:08:14.813+0000 2023-11-13T13:14:25.399+0000 true 10017714 Vándor Andrea /api/admin/10017714 Admin true 10017714 Admin 10014568 /api/admin/10014568 Vándor Andrea true 10014568 true 2024-04-18T08:04:22.531+0000 true false true 24 24 /api/publicationtype/24 PublicationType 1 true 24 JournalArticle true 10000059 Article true 24 24 /api/publicationtype/24 PublicationType 1 true 24 JournalArticle /api/subtype/10000059 Szakcikk SubType 101 true 10000059 true 1 /api/category/1 Category true 1 M., Abert Convergence of normalized Betti numbers in nonpositive curvature true true /api/journal/1351 REVIEWED true false 1351 false 1351 true 0012-7094 1547-7398 Journal FOREIGN 172 4 633 700 633 68 2023 We study the convergence of volume-normalized Betti numbers in Benjamini–Schramm convergent sequences of nonpositively curved manifolds with finite volume. In particular, we show that if X is an irreducible symmetric space of noncompact type, X ≠ ℍ3, and (Mn) is any Benjamini–Schramm convergent sequence of finite-volume X-manifolds, then the normalized Betti numbers bk(Mn)=vol(Mn) converge for all k. As a corollary, if X has higher rank and (Mn) is any sequence of distinct, finite-volume X-manifolds, then the normalized Betti numbers of Mn converge to the L2-Betti numbers of X. This extends our earlier work with Nikolov, Raimbault, and Samet, where we proved the same convergence result for uniformly thick sequences of compact X-manifolds. One of the novelties of the current work is that it applies to all quotients M D Γ\\X where Γ is arithmetic; in particular, it applies when Γ is isotropic. © 2023 Duke University Press. All rights reserved. 2023 true true true false true false GREEN 2026-02-24 true http://real.mtak.hu/163252 15 0 15 10 1 15 15 9 8 13 13 10 10 10 5 0 15 10 15 10 0 4 4 Folyóiratcikk Journal Article 24 12 Könyvrészlet Chapter in Book 25 2 Könyv Book 23 1 Egyéb konferenciaközlemény Conference paper 31 0 Egyéb konferenciakötet Conference proceedings 32 0 Oltalmi formák Protection forms 26 0 Disszertáció Thesis 28 0 Egyéb Miscellaneous 29 0 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 2018 0 1 0 1 0 2019 0 0 0 0 0 2020 0 1 1 1 1 2021 0 2 2 2 2 2022 0 2 1 2 1 2023 0 3 2 3 2 2024 0 3 2 3 2 2025 0 3 2 3 2 D1 false 10011747 false false false 2023-05-23T14:41:31.327+0000 Algebra (HRN RAMKI) 1 8 1 4 0 true 10014568 Language 10002 /api/language/10002 Angol English true 2 true PersonAuthorship 106783146 /api/authorship/106783146 1 0.25 true false Author 10011747 /api/author/10011747 Abért Miklós true 10011747 true M. Abert true false false AuthorshipType 1 /api/authorshiptype/1 0 true 0 true false true PersonAuthorship 106783147 /api/authorship/106783147 2 0.25 false false N. Bergeron true false false AuthorshipType 1 /api/authorshiptype/1 0 true 0 true false true PersonAuthorship 106783148 /api/authorship/106783148 3 0.25 false false I. Biringer true false false AuthorshipType 1 /api/authorshiptype/1 0 true 0 true false true PersonAuthorship 106783149 /api/authorship/106783149 4 0.25 false true T. Gelander true false false AuthorshipType 1 /api/authorshiptype/1 0 true 0 true false true PublicationIdentifier 24367716 /api/publicationidentifier/24367716 PlainSource 6 /api/publicationsource/6 PublicationSourceType 10001 /api/publicationsourcetype/10001 true true true DOI DOI https://doi.org/@@@ true true 6 true IDENTICAL 10.1215/00127094-2022-0029 https://doi.org/10.1215/00127094-2022-0029 false true PublicationIdentifier 23308867 /api/publicationidentifier/23308867 SwordSource 36 /api/publicationsource/36 PublicationSourceType 10007 /api/publicationsourcetype/10007 true true true REAL REAL http://real.mtak.hu/@@@ true true 36 true GREEN true 163252 http://real.mtak.hu/163252 false true PublicationIdentifier 24367717 /api/publicationidentifier/24367717 PlainSource 1 /api/publicationsource/1 PublicationSourceType 10003 /api/publicationsourcetype/10003 false true true WoS WoS https://www.webofscience.com/wos/woscc/full-record/@@@ true true 1 true IDENTICAL 000955292600001 https://www.webofscience.com/wos/woscc/full-record/000955292600001 false true PublicationIdentifier 24367718 /api/publicationidentifier/24367718 PlainSource 3 /api/publicationsource/3 PublicationSourceType 10003 /api/publicationsourcetype/10003 false true true Scopus Scopus http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-@@@ true true 3 true 85150595514 http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85150595514 false true SjrRating 11395226 /api/sjrrating/11395226 8 0.1 journal RatingType 10002 /api/ratingtype/10002 sjr true true ClassificationExternal 2601 /api/classificationexternal/2601 true 2601 true D1 DIRECT true true /api/publication/33653831 <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">M. Abert (<span class="authorship-author-name">Abért Miklós</span> <span class="authorAux-mtmt"> Csoportelmélet</span>) </a> </span> <span class="author-affil"><span title="Rényi Alfréd Matematikai Kutatóintézet">RAMKI</span>/Algebra</span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" >N. Bergeron </span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" >I. Biringer </span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" >T. Gelander </span> </div> </div> <div class="title"><a href="/gui2/?mode=browse&params=publication;33653831" target="_blank">Convergence of normalized Betti numbers in nonpositive curvature</a></div> <div> <span class="journal-title">DUKE MATHEMATICAL JOURNAL</span> <span class="journal-issn">(<a target="_blank" href="https://portal.issn.org/resource/ISSN/0012-7094">0012-7094</a> <a target="_blank" href="https://portal.issn.org/resource/ISSN/1547-7398">1547-7398</a>)</span>: <span class="journal-volume">172</span> <span class="journal-issue">4</span> <span class="page"> pp 633-700 </span> <span class="year">(2023)</span> </div> <div class="pub-footer"> <span class="language" xmlns="http://www.w3.org/1999/html">Nyelv: Angol | </span> <span class="identifiers"> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="10.1215/00127094-2022-0029" target="_blank" href="https://doi.org/10.1215/00127094-2022-0029"> DOI </a> </span> <span class="id identifier oa_GREEN" title=" Green "> <a style="color:black" title="163252" target="_blank" href="http://real.mtak.hu/163252"> REAL </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="000955292600001" target="_blank" href="https://www.webofscience.com/wos/woscc/full-record/000955292600001"> WoS </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="85150595514" target="_blank" href="http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85150595514"> Scopus </a> </span> </span> <OnlyViewableByAuthor><div class="ratings"> <div class="journal-subject">Folyóirat szakterülete: Scopus - Mathematics (miscellaneous)&nbsp;&nbsp;&nbsp;SJR indikátor:&nbsp;D1</div> </div></OnlyViewableByAuthor> <div class="publication-citation" style="margin-left: 0.5cm;"> <span title="Nyilvános idézőközlemények összesen, említések nélkül" class="citingPub-count">Nyilvános idéző összesen: 15</span> | Független: 10 | Függő: 5 | Nem jelölt: 0 | WoS jelölt: 9 | Scopus jelölt:&nbsp;8 | WoS/Scopus jelölt:&nbsp;13 | DOI jelölt:&nbsp;15 </div> <div class="publication-citation"> <a target="_blank" href="/api/publication?cond=citations.related;eq;33653831&sort=publishedYear,desc&sort=title"> Idézett közlemények száma: 4 </a> </div> <div class="mtid"><span class="long-pub-mtid">Közlemény: 33653831</span> | <span class="status-data status-ADMIN_APPROVED"> Admin láttamozott </span> Forrás Idéző | <span class="type-subtype">Folyóiratcikk ( Szakcikk ) </span> | <span class="pub-category">Tudományos</span> | <span class="publication-sourceOfData">kézi felvitel</span> </div> <div class="lastModified">Utolsó módosítás: 2024.01.15. 16:18 Wolf György (MTMT Központi admin) </div> <div class="lockedBy">Központi kezelésű 2024.04.18. 10:04 Vándor Andrea (VA, admin) </div> <pre class="comment" style="margin-top: 0; margin-bottom: 0;"><u>Megjegyzés</u>: Export Date: 13 September 2023 Funding details: National Science Foundation, NSF, DMS-1611851, DMS-1654114 Funding details: European Research Council, ERC, 648017 Funding details: Israel Science Foundation, ISF, 2095/15 Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, K1096...</pre> </div></div>