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The action functional on dual Legendrian submanifolds of the loop space of a contact three dimensional closed manifold
Descriptive
TitleInfo
Title
The action functional on dual Legendrian submanifolds of the loop space of a contact three dimensional closed manifold
Name
(type = personal)
NamePart
(type = family)
Maalaoui
NamePart
(type = given)
Ali
NamePart
(type = date)
1983-
DisplayForm
Ali Maalaoui
Role
RoleTerm
(authority = RULIB)
author
Name
(type = personal)
NamePart
(type = family)
Bahri
NamePart
(type = given)
Abbas
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Abbas Bahri
Affiliation
Advisory Committee
Role
RoleTerm
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chair
Name
(type = personal)
NamePart
(type = family)
Chanillo
NamePart
(type = given)
Sagun
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Sagun Chanillo
Affiliation
Advisory Committee
Role
RoleTerm
(authority = RULIB)
internal member
Name
(type = personal)
NamePart
(type = family)
Woodward
NamePart
(type = given)
Christopher
DisplayForm
Christopher Woodward
Affiliation
Advisory Committee
Role
RoleTerm
(authority = RULIB)
internal member
Name
(type = personal)
NamePart
(type = family)
Masmoudi
NamePart
(type = given)
Nader
DisplayForm
Nader Masmoudi
Affiliation
Advisory Committee
Role
RoleTerm
(authority = RULIB)
outside member
Name
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NamePart
Rutgers University
Role
RoleTerm
(authority = RULIB)
degree grantor
Name
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NamePart
Graduate School - New Brunswick
Role
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(authority = RULIB)
school
TypeOfResource
Text
Genre
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theses
OriginInfo
DateCreated
(qualifier = exact)
2013
DateOther
(qualifier = exact);
(type = degree)
2013-05
Place
PlaceTerm
(type = code)
xx
Language
LanguageTerm
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(type = code)
eng
Abstract
(type = abstract)
The main object of my dissertation is the study of the action functional of a contact form on a three dimensional manifold. This is part of a long program started by Professor A. Bahri [3], [4] in constructing a contact homology giving information about the number of periodic orbits of the Reeb vector field, that is an attempt to approach the Weinstein conjecture for 3-manifolds. Even though it appears to be proved by C. Taubes in a series of paper (see for instance [39] for more details). Given a closed 3-dimensional manifold, we prove an S1 homotopy equivalence between a subspace Cß of Legendrian curves and the free loop space. This space appears to be convenient from a variational point of view, in contact form geometry and used in the approach developed by A. Bahri. Indeed, it is the right space of variations on which we study the action functional. In a second part we study the Fredholm assumption for a modifed version of the action functional on the variational space Cß. That is, whether the functional is Fredholm or not. We take here the text-book case-study of a sequence of overtwisted contact forms on the 3-sphere introduced by Gonzalo and Varela [26]. We show that the Fredholm assumption does not hold. This is done by studying the dynamics of the contact form along a vector field on its kernel. We also prove the existence of a foliation stuck between the contact form and its Legendre dual in the part where they have opposite orientation. In the last part we present an explicit computation of the Bahri contact homology for a sequence of tight contact structures in the torus. We also extend this result to the case of torus bundles over S1. The homology that we find, allows us in particular to confirm the fact that the contact structures are not isotopic since it has different values for each structure.
Subject
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Topic
Mathematics
RelatedItem
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TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier
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ETD
Identifier
ETD_4635
PhysicalDescription
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electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
ix, 122 p. : ill.
Note
(type = degree)
Ph.D.
Note
(type = bibliography)
Includes bibliographical references
Note
(type = vita)
Includes vita
Note
(type = statement of responsibility)
by Ali Maalaoui
Subject
(authority = ETD-LCSH)
Topic
Three-manifolds (Topology)
Subject
(authority = ETD-LCSH)
Topic
Manifolds (Mathematics)
Identifier
(type = hdl)
http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000069045
RelatedItem
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TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier
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rucore19991600001
Location
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(displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier
(type = doi)
doi:10.7282/T34748FD
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
Maalaoui
GivenName
Ali
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime
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(qualifier = exact);
(point = start)
2013-04-11 12:48:23
AssociatedEntity
Name
Ali Maalaoui
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
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Copyright protected
Availability
Status
Open
Reason
Permission or license
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Technical
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ETD
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windows xp
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