Staff View
Constructing and classifying fully irreducible outer automorphisms of free groups

Descriptive

TitleInfo
Title
Constructing and classifying fully irreducible outer automorphisms of free groups
Name (type = personal)
NamePart (type = family)
Pfaff
NamePart (type = given)
Catherine
NamePart (type = date)
1982-
DisplayForm
Catherine Pfaff
Role
RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
Mosher
NamePart (type = given)
Lee
DisplayForm
Lee Mosher
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
chair
Name (type = personal)
NamePart (type = family)
Luo
NamePart (type = given)
Feng
DisplayForm
Feng Luo
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Carbone
NamePart (type = given)
Lisa
DisplayForm
Lisa Carbone
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Feighn
NamePart (type = given)
Mark
DisplayForm
Mark Feighn
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)
2012
DateOther (qualifier = exact); (type = degree)
2012-10
Place
PlaceTerm (type = code)
xx
Language
LanguageTerm (authority = ISO639-2b); (type = code)
eng
Abstract (type = abstract)
The main theorem of this document emulates, in the context of Out(F_r) theory, a mapping class group theorem (by H. Masur and J. Smillie) that determines precisely which index lists arise from pseudo-Anosov mapping classes. Since the ideal Whitehead graph gives a finer invariant in the analogous setting of a fully irreducible outer automorphisms of free groups, we instead focus on determining which of the twenty-one connected, loop-free, five-vertex graphs are ideal Whitehead graphs of ageometric, fully irreducible outer automorphisms of free groups in rank three. Our main theorem accomplishes this by showing that there are precisely eighteen graphs arising as such. We also give a method for identifying certain complications called periodic Nielsen paths, prove the existence of conveniently decomposed representatives of ageometric, fully irreducible outer automorphisms of free groups having connected, (2r-1)-vertex ideal Whitehead graphs, and prove a criterion for identifying representatives of ageometric, fully irreducible outer automorphisms of free groups. The strategies we use for constructing fully irreducible outer automorphisms of free groups, as well as our identification and decomposition techniques, can be used to extend our main theorem, as they are valid in any rank. Our methods of proof rely primarily on Bestvina-Feighn-Handel train track theory and the theory of attracting laminations.
Subject (authority = RUETD)
Topic
Mathematics
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_4303
PhysicalDescription
Form (authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
xiv, 190 p. : ill.
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Catherine Pfaff
Subject (authority = ETD-LCSH)
Topic
Geometric group theory
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000066937
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/T30R9N56
Genre (authority = ExL-Esploro)
ETD doctoral
Back to the top

Rights

RightsDeclaration (ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
Pfaff
GivenName
Catherine
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2012-09-27 11:24:54
AssociatedEntity
Name
Catherine Pfaff
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
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
Back to the top

Technical

FileSize (UNIT = bytes)
1057792
OperatingSystem (VERSION = 5.1)
windows xp
ContentModel
ETD
MimeType (TYPE = file)
application/pdf
MimeType (TYPE = container)
application/x-tar
FileSize (UNIT = bytes)
1064960
Checksum (METHOD = SHA1)
e14b7a775807daf716dac2a9791dc92e9436b4f4
Back to the top
Version 8.5.5
Rutgers University Libraries - Copyright ©2024