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dc.contributor.advisorShalen, Peter B.en_US
dc.contributor.authorGuzman, Rosemary K.en_US
dc.date.accessioned2012-12-07T11:56:15Z
dc.date.available2014-04-15T09:30:43Z
dc.date.created2011-08en_US
dc.date.issued2012-12-07
dc.date.submitted2011-08en_US
dc.identifier.urihttp://hdl.handle.net/10027/8926
dc.description.abstractThe results of Marc Culler and Peter Shalen for 2,3 or 4-free hyperbolic 3-manifolds are contingent on properties specific to and special about rank two subgroups of a free group. Here we determine what construction and algebraic information is required in order to make a geometric statement about M a closed, orientable hyperbolic manifold with k-free fundamental group for any value of k greater than four. Main results are both to show what the formulation of the general statement should be, for which Culler and Shalen’s result is a special case, and that it is true modulo a group-theoretic conjecture. A major result is in the k = 5 case of the geometric statement. Specifically, I show that the required group-theoretic conjecture is in fact true in this case, and so the proposed geometric statement when M is 5-free is indeed a theorem. One can then use the existence of a point and knowledge about π1(M,P) resulting from this theorem to attempt to improve the known lower bound on the volume of M, which is currently 3.44 (Culler, Shalen).en_US
dc.language.isoenen_US
dc.rightsen_US
dc.rightsCopyright 2011 Rosemary K. Guzmanen_US
dc.subjecthyperbolic 3-manifoldsen_US
dc.subjectk-freeen_US
dc.subject4-freeen_US
dc.subjectfundamental groupen_US
dc.subjectactions without inversions on a treeen_US
dc.subjectrank-3 subgroups of a free groupen_US
dc.subject5-freeen_US
dc.titleHyperbolic 3-manifolds with k-free fundamental groupen_US
thesis.degree.departmentMathematicsen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Illinois at Chicagoen_US
thesis.degree.levelDoctoralen_US
thesis.degree.namePhD, Doctor of Philosophyen_US
dc.type.genrethesisen_US
dc.contributor.committeeMemberCuller, Marcen_US
dc.contributor.committeeMemberShipley, Brookeen_US
dc.contributor.committeeMemberCanary, Richard D.en_US
dc.contributor.committeeMemberFarb, Bensonen_US
dc.type.materialtexten_US


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