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Linking and discreteness in hyperbolic 4-space
Descriptive
TitleInfo
Title
Linking and discreteness in hyperbolic 4-space
Name
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NamePart
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Silverio
NamePart
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Andrew Ebitner
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Andrew Silverio
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(authority = RULIB)
author
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(type = personal)
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Gilman
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(type = given)
Jane P
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Jane P Gilman
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Advisory Committee
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chair
Name
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Loftin
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John C
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John C Loftin
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Advisory Committee
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internal member
Name
(type = personal)
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(type = family)
Feighn
NamePart
(type = given)
Mark E
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Mark E Feighn
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Advisory Committee
Role
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(authority = RULIB)
internal member
Name
(type = personal)
NamePart
(type = family)
Luo
NamePart
(type = given)
Feng
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Feng Luo
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Advisory Committee
Role
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(authority = RULIB)
outside member
Name
(type = personal)
NamePart
(type = family)
Keen
NamePart
(type = given)
Linda
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Linda Keen
Affiliation
Advisory Committee
Role
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(authority = RULIB)
outside member
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NamePart
Rutgers University
Role
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(authority = RULIB)
degree grantor
Name
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NamePart
Graduate School - Newark
Role
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school
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Text
Genre
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theses
OriginInfo
DateCreated
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2013
DateOther
(qualifier = exact);
(type = degree)
2013-05
Place
PlaceTerm
(type = code)
xx
Language
LanguageTerm
(authority = ISO639-2b);
(type = code)
eng
Abstract
(type = abstract)
A pair of isometries of the 4-dimensional hyperbolic space is called linked if they can be expressed as compositions of two involutions, one of which is common to both isometries. While every pair of isometries of hyperbolic space in dimensions 2 and 3 is linked, not all pairs of isometries of hyperbolic 4-space are linked. One type of such an involution is called half-turn which is an orientation preserving elliptic isometry with a 2-dimensional fixed point set. We provide some geometric conditions for such a pair to be linked by half-turns. Here we develop a theory of pencils, twisting planes and half-turn banks that gives results about each of the pair-types of isometries and their simultaneous factorization. In order to provide conditions under which a given pair is linked via a half-turn, sets of hyperplanes in hyperbolic 4-space are defined for each orientation preserving isometry that enables one to locate the half-turns for which linking is possible. Once a pair is linked, known conditions about discreteness of the group, generated by a pair of isometries, in lower dimensional hyperbolic spaces can be generalized to some linked pairs in dimension 4. If a pair has a common invariant hyperplane or plane, the known conditions such as compact-core-geodesic-intersection and non-separating-disjoint-circles apply.
Subject
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Topic
Mathematical Sciences
RelatedItem
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TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier
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ETD
Identifier
ETD_4741
PhysicalDescription
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electronic resource
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application/pdf
InternetMediaType
text/xml
Extent
ix, 155 p. : ill.
Note
(type = degree)
Ph.D.
Note
(type = bibliography)
Includes bibliographical references
Note
(type = vita)
Includes vita
Note
(type = statement of responsibility)
by Andrew Ebitner Silverio
Subject
(authority = ETD-LCSH)
Topic
Hyperbolic spaces
Subject
(authority = ETD-LCSH)
Topic
Discrete groups
Identifier
(type = hdl)
http://hdl.rutgers.edu/1782.1/rucore10002600001.ETD.000068778
RelatedItem
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TitleInfo
Title
Graduate School - Newark Electronic Theses and Dissertations
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rucore10002600001
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(displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier
(type = doi)
doi:10.7282/T3FX7829
Genre
(authority = ExL-Esploro)
ETD doctoral
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Rights
RightsDeclaration
(ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder
(type = personal)
Name
FamilyName
Silverio
GivenName
Andrew
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime
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(qualifier = exact);
(point = start)
2013-04-23 22:54:14
AssociatedEntity
Name
Andrew Silverio
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - Newark
AssociatedObject
Type
License
Name
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.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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Technical
RULTechMD
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ContentModel
ETD
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windows xp
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