Isometries of length 1 in purely loxodromic free kleinian groups and trace inequalities

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dc.contributor.authorYuce, Ilker Savas
dc.contributor.authorNarman, Ahmet Nedim
dc.date.accessioned2024-07-18T20:50:47Z
dc.date.available2024-07-18T20:50:47Z
dc.date.issued2024
dc.departmentİstanbul Bilgi Üniversitesien_US
dc.description.abstractIn this paper, we prove a generalization of a discreteness criteria for a large class of subgroups of PSL 2(C). In particular, given a finitely generated purely loxodromic free Kleinian group Gamma = for n >= 2, we show that |trace(2) (xi(i)) - 4| + |trace(xi(i)xi(j)xi(-1)(i) xi(-1)(j)) - 2| >= 2 sinh(2) ( 1/4 log alpha(n)) for some xi(i) and xi(j) for i not equal j in Gamma provided that certain conditions on the hyperbolic displacements given by xi(i), xi(j) and their length 3 conjugates formed by the generators are satisfied. Above, the constant alpha(n) turns out to be the real root strictly larger than (2n-1)(2) of a fourth degree integer coefficient polynomial obtained by solving a family of optimization problems via the Karush-Kuhn-Tucker theory. The use of this theory in the context of hyperbolic geometry is another novelty of this work.en_US
dc.identifier.doi10.55730/1300-0098.3501
dc.identifier.issn1300-0098
dc.identifier.issn1303-6149
dc.identifier.issue2en_US
dc.identifier.scopus2-s2.0-85188992578en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.urihttps://doi.org/10.55730/1300-0098.3501
dc.identifier.urihttps://hdl.handle.net/11411/8237
dc.identifier.volume48en_US
dc.identifier.wosWOS:001188914500009en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherTubitak Scientific & Technological Research Council Turkeyen_US
dc.relation.ispartofTurkish Journal of Mathematicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectFree Kleinian Groupsen_US
dc.subjectJorgensen's İnequalityen_US
dc.subjectTrace İnequalitiesen_US
dc.subjectHyperbolic Displacementsen_US
dc.subjectLog 3 Theoremen_US
dc.subjectKarush-Kuhn-Tucker Theoryen_US
dc.subjectDeformation Spacesen_US
dc.subjectBoundariesen_US
dc.titleIsometries of length 1 in purely loxodromic free kleinian groups and trace inequalities
dc.typeArticle

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