{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,22]],"date-time":"2023-08-22T22:09:57Z","timestamp":1692742197543},"reference-count":19,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2008,5]]},"abstract":"<jats:p> We consider the question of which right-angled Artin groups contain closed hyperbolic surface subgroups. It is known that a right-angled Artin group A(K) has such a subgroup if its defining graph K contains an n-hole (i.e. an induced cycle of length n) with n \u2265 5. We construct another eight \"forbidden\" graphs and show that every graph K on \u2264 8 vertices either contains one of our examples, or contains a hole of length \u2265 5, or has the property that A(K) does not contain hyperbolic closed surface subgroups. We also provide several sufficient conditions for a right-angled Artin group to contain no hyperbolic surface subgroups. <\/jats:p><jats:p> We prove that for one of these \"forbidden\" subgraphs P<jats:sub>2<\/jats:sub>(6), the right-angled Artin group A(P<jats:sub>2<\/jats:sub>(6)) is a subgroup of a (right-angled Artin) diagram group. Thus we show that a diagram group can contain a non-free hyperbolic subgroup answering a question of Guba and Sapir. We also show that fundamental groups of non-orientable surfaces can be subgroups of diagram groups. Thus the first integral homology of a subgroup of a diagram group can have torsion (all homology groups of all diagram groups are free Abelian by a result of Guba and Sapir). <\/jats:p>","DOI":"10.1142\/s0218196708004536","type":"journal-article","created":{"date-parts":[[2008,6,2]],"date-time":"2008-06-02T10:26:32Z","timestamp":1212402392000},"page":"443-491","source":"Crossref","is-referenced-by-count":14,"title":["SURFACE SUBGROUPS OF RIGHT-ANGLED ARTIN GROUPS"],"prefix":"10.1142","volume":"18","author":[{"given":"JOHN","family":"CRISP","sequence":"first","affiliation":[{"name":"I.M.B. (UMR 5584 du CNRS), Universit\u00e9 de Bourgogne, B.P. 47 870, 21078 Dijon, France"}]},{"given":"MICHAH","family":"SAGEEV","sequence":"additional","affiliation":[{"name":"Technion, Israel University of Technology, Department of Mathematics, Haifa 32000, Israel"}]},{"given":"MARK","family":"SAPIR","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8369-7_1"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01388519"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.2140\/agt.2004.4.439"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1987-0891135-1"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(99)00175-9"},{"key":"rf7","first-page":"71","volume":"38","author":"Dirac G. A.","journal-title":"Abh. Math. 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Olshanskii A.","journal-title":"Sibirsk. Mat. Zh."},{"key":"rf25","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-3618-1"},{"key":"rf26","first-page":"779","volume":"48","author":"Razborov A. A.","journal-title":"Izv. Akad. Nauk SSSR Ser. Mat."}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196708004536","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T22:28:00Z","timestamp":1565130480000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196708004536"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,5]]},"references-count":19,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2008,5]]}},"alternative-id":["10.1142\/S0218196708004536"],"URL":"https:\/\/doi.org\/10.1142\/s0218196708004536","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,5]]}}}