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Their proof relied on machinery only available in the [Formula: see text] case, namely, Thurston\u2019s piecewise-projective model for Thompson\u2019s group T, so, our approach necessarily utilizes different tools. This also provides an alternate proof of Haagerup\u2013Olesen\u2019s result when [Formula: see text].<\/jats:p>","DOI":"10.1142\/s0218196725500365","type":"journal-article","created":{"date-parts":[[2025,7,25]],"date-time":"2025-07-25T06:25:02Z","timestamp":1753424702000},"page":"1123-1134","source":"Crossref","is-referenced-by-count":0,"title":["Non-inner amenability of the Higman\u2013Thompson groups"],"prefix":"10.1142","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-6056-4070","authenticated-orcid":false,"given":"Eli","family":"Bashwinger","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Utah, Salt Lake City, UT 84112, United States"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2993-5777","authenticated-orcid":false,"given":"Matthew C.\u00a0B.","family":"Zaremsky","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University at Albany (SUNY), Albany 12222, New York, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2025,8,19]]},"reference":[{"key":"S0218196725500365BIB001","doi-asserted-by":"publisher","DOI":"10.4171\/GGD\/207"},{"key":"S0218196725500365BIB002","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-08-04381-X"},{"key":"S0218196725500365BIB003","doi-asserted-by":"publisher","DOI":"10.24033\/asens.2462"},{"key":"S0218196725500365BIB004","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196711006571"},{"key":"S0218196725500365BIB005","first-page":"45","volume-title":"Proc. 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