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Factorization of isometries of hyperbolic 4-space and a discreteness condition

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TypeOfResource
Text
TitleInfo (ID = T-1)
Title
Factorization of isometries of hyperbolic 4-space and a discreteness condition
SubTitle
PartName
PartNumber
NonSort
Identifier (displayLabel = ); (invalid = )
ETD_1793
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.2/rucore10002600001.ETD.000051314
Language (objectPart = )
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eng
Genre (authority = marcgt)
theses
Subject (ID = SBJ-1); (authority = RUETD)
Topic
Mathematical Sciences
Subject (ID = SBJ-2); (authority = ETD-LCSH)
Topic
Differential equations
Subject (ID = SBJ-3); (authority = ETD-LCSH)
Topic
Discrete groups
Subject (ID = SBJ-4); (authority = ETD-LCSH)
Topic
Factorization (Mathematics)
Abstract
Gilman'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.
PhysicalDescription
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electronic resource
Extent
vi, 54 p. : ill.
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application/pdf
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Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references (p. 52-53)
Note (type = statement of responsibility)
by Karan Mohan Puri
Name (ID = NAME-1); (type = personal)
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Puri
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Karan Mohan
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1981
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Karan Mohan Puri
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Gilman
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chair
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Jane P. Gilman
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Mark
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Mark Feighn
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Mosher
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Lee
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internal member
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Lee Mosher
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Basmajian
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Ara
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outside member
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Advisory Committee
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Ara Basmajian
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NamePart
Rutgers University
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degree grantor
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Graduate School - Newark
Role
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school
OriginInfo
DateCreated (point = ); (qualifier = exact)
2009
DateOther (qualifier = exact); (type = degree)
2009-05
Place
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xx
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TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
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Title
Graduate School - Newark Electronic Theses and Dissertations
Identifier (type = local)
rucore10002600001
Location
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NjNbRU
Identifier (type = doi)
doi:10.7282/T3WQ0402
Genre (authority = ExL-Esploro)
ETD doctoral
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Rights

RightsDeclaration (AUTHORITY = GS); (ID = rulibRdec0006)
The author owns the copyright to this work.
Copyright
Status
Copyright protected
Notice
Note
Availability
Status
Open
Reason
Permission or license
Note
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Name
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Puri
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Karan
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Copyright holder
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Karan Puri
Affiliation
Rutgers University. Graduate School - Newark
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License
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Author Agreement License
Detail
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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Technical

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337920
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