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Low-lying geodesics in an arithmetic hyperbolic three-manifold
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McKeon, Katie Lynn. Low-lying geodesics in an arithmetic hyperbolic three-manifold. Retrieved from https://doi.org/doi:10.7282/t3-cj23-rp08

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TitleLow-lying geodesics in an arithmetic hyperbolic three-manifold
NameMcKeon, Katie Lynn (author); Kontorovich, Alex (chair); Iwaniec, Henryk (internal member); Tunnell, Jerrold (internal member); Pierce, Lillian (outside member); Rutgers University; School of Graduate Studies
Date Created2018
Other Date2018-10 (degree)
SubjectMathematics, Three-manifolds (Topology), Geodesics (Mathematics)
Extent1 online resource (76 pages) : illustrations
DescriptionWe examine closed geodesics in the quotient of hyperbolic three space by the discrete group of isometries SL(2,Z[i]). There is a correspondence between closed geodesics in the manifold, the complex continued fractions originally studied by Hurwitz, and binary quadratic forms over the Gaussian integers. According to this correspondence, a geodesic is called fundamental if the associated binary quadratic form is. Using techniques from sieve theory, symbolic dynamics, and the theory of expander graphs, we show the existence of a compact set in the manifold containing infinitely many fundamental geodesics.
NotePh.D.
NoteIncludes bibliographical references
Noteby Katie Lynn McKeon
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/t3-cj23-rp08
Languageeng
CollectionSchool of Graduate Studies Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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