{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T14:09:42Z","timestamp":1762870182656,"version":"build-2065373602"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","issue":"7","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Eur. Math. Soc."],"published-print":{"date-parts":[[2014,8,23]]},"abstract":"<jats:p>\n                    Let\n                    <jats:inline-formula>\n                      <jats:tex-math>2 \\leq a \\leq b \\leq c \\in \\mathbb{N}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    with\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mu=1\/a+1\/b+1\/c&lt;1<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    and let\n                    <jats:inline-formula>\n                      <jats:tex-math>T=T_{a,b,c}=\\langle x,y,z: x^a=y^b=z^c=xyz=1\\rangle<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    be the corresponding hyperbolic triangle group. Many papers have been dedicated to the following question: what are the finite (simple) groups which appear as quotients of\n                    <jats:inline-formula>\n                      <jats:tex-math>T<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    ? (Classically, for\n                    <jats:inline-formula>\n                      <jats:tex-math>(a,b,c)=(2,3,7)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    and more recently also for general\n                    <jats:inline-formula>\n                      <jats:tex-math>(a,b,c)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    .) These papers have used either explicit constructive methods or probabilistic ones. The goal of this paper is to present a new approach based on the theory of representation varieties (via deformation theory). As a corollary we essentially prove a conjecture of Marion [21] showing that various finite simple groups are not quotients of\n                    <jats:inline-formula>\n                      <jats:tex-math>T<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , as well as positive results showing that many finite simple groups are quotients of\n                    <jats:inline-formula>\n                      <jats:tex-math>T<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    .\n                  <\/jats:p>","DOI":"10.4171\/jems\/463","type":"journal-article","created":{"date-parts":[[2014,8,23]],"date-time":"2014-08-23T17:45:12Z","timestamp":1408815912000},"page":"1349-1375","source":"Crossref","is-referenced-by-count":10,"title":["Deformation theory and finite simple quotients of triangle groups I"],"prefix":"10.4171","volume":"16","author":[{"given":"Michael","family":"Larsen","sequence":"first","affiliation":[{"name":"Indiana University, Bloomington, United States"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7281-1142","authenticated-orcid":false,"given":"Alexander","family":"Lubotzky","sequence":"additional","affiliation":[{"name":"Hebrew University, Jerusalem, Israel"}]},{"given":"Claude","family":"Marion","sequence":"additional","affiliation":[{"name":"Hebrew University, Jerusalem, Israel"}]}],"member":"2673","container-title":["Journal of the European Mathematical Society"],"original-title":[],"link":[{"URL":"http:\/\/www.ems-ph.org\/fulltext\/10.4171\/JEMS\/463","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T13:59:30Z","timestamp":1762869570000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/jems\/463"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,8,23]]},"references-count":0,"journal-issue":{"issue":"7"},"URL":"https:\/\/doi.org\/10.4171\/jems\/463","relation":{},"ISSN":["1435-9855","1435-9863"],"issn-type":[{"type":"print","value":"1435-9855"},{"type":"electronic","value":"1435-9863"}],"subject":[],"published":{"date-parts":[[2014,8,23]]}}}