{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T05:11:17Z","timestamp":1648876277742},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2018,8]]},"abstract":"<jats:p> In this paper, we study the quotient and \u201cblow-up\u201d of graph-of-groups [Formula: see text] and of their automorphisms [Formula: see text]. We show that the existence of such a blow-up of any [Formula: see text], relative to a given family of \u201clocal\u201d graph-of-groups isomorphisms [Formula: see text] depends crucially on the [Formula: see text]-conjugacy class of the correction term [Formula: see text] for any edge [Formula: see text] of [Formula: see text], where [Formula: see text]-conjugacy is a new but natural concept introduced here. <\/jats:p><jats:p> As an application, we obtain a criterion as to whether a partial Dehn twist can be blown up relative to local Dehn twists, to give an actual Dehn twist. The results of this paper are also used crucially in the follow-up papers [Lustig and Ye, Normal form and parabolic dynamics for quadratically growing automorphisms of free groups, arXiv:1705.04110v2; Ye, Partial Dehn twists of free groups relative to local Dehn twists \u2014 A dichotomy, arXiv:1605.04479 ; When is a polynomially growing automorphism of [Formula: see text] geometric, arXiv:1605.07390 ]. <\/jats:p>","DOI":"10.1142\/s0218196718500340","type":"journal-article","created":{"date-parts":[[2018,5,7]],"date-time":"2018-05-07T07:47:21Z","timestamp":1525679241000},"page":"733-758","source":"Crossref","is-referenced-by-count":0,"title":["Quotient and blow-up of automorphisms of graphs of groups"],"prefix":"10.1142","volume":"28","author":[{"given":"Kaidi","family":"Ye","sequence":"first","affiliation":[{"name":"KU Leuven, Department of Mathematics, Campus Kulak Kortrijk, E. Sabbelaan 53, 8500 Kortrijk, Belgium"}]}],"member":"219","published-online":{"date-parts":[[2018,8,17]]},"reference":[{"key":"S0218196718500340BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(93)90085-8"},{"key":"S0218196718500340BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(95)00134-4"},{"key":"S0218196718500340BIB004","doi-asserted-by":"publisher","DOI":"10.2307\/2946562"},{"key":"S0218196718500340BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"S0218196718500340BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s00039-010-0072-9"},{"key":"S0218196718500340BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/0040-9383(94)00038-M"},{"key":"S0218196718500340BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/s000140050085"},{"key":"S0218196718500340BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/s10711-004-1492-1"},{"key":"S0218196718500340BIB013","volume-title":"Combinatorial Group Theory","author":"Lyndon R. C.","year":"1997"},{"key":"S0218196718500340BIB015","doi-asserted-by":"publisher","DOI":"10.1007\/BF01896245"},{"key":"S0218196718500340BIB016","doi-asserted-by":"publisher","DOI":"10.2307\/2951832"},{"key":"S0218196718500340BIB018","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004115000225"},{"key":"S0218196718500340BIB019","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61856-7"},{"key":"S0218196718500340BIB020","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(86)90032-0"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196718500340","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T13:17:25Z","timestamp":1565097445000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196718500340"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8]]},"references-count":14,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2018,8,17]]},"published-print":{"date-parts":[[2018,8]]}},"alternative-id":["10.1142\/S0218196718500340"],"URL":"https:\/\/doi.org\/10.1142\/s0218196718500340","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8]]}}}