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Quantifying algebraic properties of surface groups and 3-manifold groups
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Patel, Priyam. Quantifying algebraic properties of surface groups and 3-manifold groups. Retrieved from https://doi.org/doi:10.7282/T3HT2MXB

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TitleQuantifying algebraic properties of surface groups and 3-manifold groups
NamePatel, Priyam (author); Luo, Feng (chair); Rong, Xiaochun (internal member); Ferry, Steven (internal member); McReynolds, David Ben (outside member); Rutgers University; Graduate School - New Brunswick
Date Created2013
Other Date2013-05 (degree)
SubjectMathematics, Hyperbolic groups, Manifolds (Mathematics)
Extentvi, 46 p. : ill.
DescriptionA group G is residually finite (RF) if for every nontrivial element g in G, there exists a finite index subgroup G' of G such that g is not in G'. A group G is called locally extended residually finite (LERF) if for any finitely generated subgroup S of G and any g in G -S, there exists a finite index subgroup G' of G which contains S but not g. Quantifying these algebraic finiteness properties refers to bounding the indexes of the finite index subgroups G' in each of the definitions above. In this dissertation we quantify Peter Scott's theorem that surface groups are LERF in terms of geometric data. In the process, we will quantify the fact that surface groups are residually finite and quantify another result by Scott that any closed geodesic in a surface lifts to an embedded loop in a finite cover. We also extend the methods used in the 2-dimensional case to quantify the residual finiteness of particular 3-manifold groups.
NotePh.D.
NoteIncludes bibliographical references
NoteIncludes vita
Noteby Priyam Patel
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/T3HT2MXB
Languageeng
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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