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Quantifying algebraic properties of surface groups and 3-manifold groups

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TitleInfo
Title
Quantifying algebraic properties of surface groups and 3-manifold groups
Name (type = personal)
NamePart (type = family)
Patel
NamePart (type = given)
Priyam
DisplayForm
Priyam Patel
Role
RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
Luo
NamePart (type = given)
Feng
DisplayForm
Feng Luo
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
chair
Name (type = personal)
NamePart (type = family)
Rong
NamePart (type = given)
Xiaochun
DisplayForm
Xiaochun Rong
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Ferry
NamePart (type = given)
Steven
DisplayForm
Steven Ferry
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
McReynolds
NamePart (type = given)
David Ben
DisplayForm
David Ben McReynolds
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
outside member
Name (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (type = corporate)
NamePart
Graduate School - New Brunswick
Role
RoleTerm (authority = RULIB)
school
TypeOfResource
Text
Genre (authority = marcgt)
theses
OriginInfo
DateCreated (qualifier = exact)
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 group G is residually finite (RF) if for every nontrivial element g in G, there exists a finite index subgroup G' of G such that g is not in G'. A group G is called locally extended residually finite (LERF) if for any finitely generated subgroup S of G and any g in G -S, there exists a finite index subgroup G' of G which contains S but not g. Quantifying these algebraic finiteness properties refers to bounding the indexes of the finite index subgroups G' in each of the definitions above. In this dissertation we quantify Peter Scott's theorem that surface groups are LERF in terms of geometric data. In the process, we will quantify the fact that surface groups are residually finite and quantify another result by Scott that any closed geodesic in a surface lifts to an embedded loop in a finite cover. We also extend the methods used in the 2-dimensional case to quantify the residual finiteness of particular 3-manifold groups.
Subject (authority = RUETD)
Topic
Mathematics
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_4612
PhysicalDescription
Form (authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
vi, 46 p. : ill.
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = vita)
Includes vita
Note (type = statement of responsibility)
by Priyam Patel
Subject (authority = ETD-LCSH)
Topic
Hyperbolic groups
Subject (authority = ETD-LCSH)
Topic
Manifolds (Mathematics)
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000068933
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier (type = doi)
doi:10.7282/T3HT2MXB
Genre (authority = ExL-Esploro)
ETD doctoral
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RightsDeclaration (ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
Patel
GivenName
Priyam
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2013-04-10 00:04:32
AssociatedEntity
Name
Priyam Patel
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
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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
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Copyright protected
Availability
Status
Open
Reason
Permission or license
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RULTechMD (ID = TECHNICAL1)
ContentModel
ETD
OperatingSystem (VERSION = 5.1)
windows xp
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