{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T19:17:35Z","timestamp":1773256655414,"version":"3.50.1"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2014,3]]},"abstract":"<jats:p>We develop an analogy between right-angled Artin groups and mapping class groups through the geometry of their actions on the extension graph and the curve graph, respectively. The central result in this paper is the fact that each right-angled Artin group acts acylindrically on its extension graph. From this result, we are able to develop a Nielsen\u2013Thurston classification for elements in the right-angled Artin group. Our analogy spans both the algebra regarding subgroups of right-angled Artin groups and mapping class groups, as well as the geometry of the extension graph and the curve graph. On the geometric side, we establish an analogue of Masur and Minsky's Bounded Geodesic Image Theorem and their distance formula.<\/jats:p>","DOI":"10.1142\/s021819671450009x","type":"journal-article","created":{"date-parts":[[2014,3,11]],"date-time":"2014-03-11T12:23:47Z","timestamp":1394540627000},"page":"121-169","source":"Crossref","is-referenced-by-count":47,"title":["The geometry of the curve graph of a right-angled Artin group"],"prefix":"10.1142","volume":"24","author":[{"given":"Sang-Hyun","family":"Kim","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Korea"}]},{"given":"Thomas","family":"Koberda","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Yale University, 20 Hillhouse Ave, New Haven, CT 06520, USA"}]}],"member":"219","published-online":{"date-parts":[[2014,4,10]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.2140\/gt.2009.13.2523"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01917515"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.2140\/gt.2012.16.781"},{"key":"rf5","doi-asserted-by":"crossref","first-page":"681","DOI":"10.4171\/ggd\/100","volume":"4","author":"Behrstock J. 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