TitleFactorization of isometries of hyperbolic 4-space and a discreteness condition
NamePuri, Karan Mohan (author), Gilman, Jane (chair), Feighn, Mark (internal member), Mosher, Lee (internal member), Basmajian, Ara (outside member), Rutgers University, Graduate School - Newark,
DescriptionGilman's NSDC condition is a sufficient condition for the discreteness of a two generator subgroup of PSL(2,C). We address the question of the extension of this condition to subgroups of isometries of hyperbolic 4-space. While making this new construction, namely the NSDS condition, we are led to ask whether every orientation preserving isometry of hyperbolic 4-space can be factored into the product of two half-turns. We use some techniques developed by Wilker to first, define a half-turn suitably in dimension 4 and then answer the former question. It turns out that defining a half-turn in this way in any dimension n enables us to generalize some of Gilman's theorems to dimension greater than or equal to 4. We also give an exposition on part of Wilker's work and give new proofs for some of his results.
NoteIncludes bibliographical references (p. 52-53)
Noteby Karan Mohan Puri
CollectionGraduate School - Newark Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.