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The skein algebra of arcs and links and the decorated Teichmüller space
Descriptive
TitleInfo
Title
The skein algebra of arcs and links and the decorated Teichmüller space
Name
(type = personal)
NamePart
(type = family)
Yang
NamePart
(type = given)
Tian
NamePart
(type = date)
1982-
DisplayForm
Tian Yang
Role
RoleTerm
(authority = RULIB)
author
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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chair
Name
(type = personal)
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(type = family)
Ferry
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(type = given)
Steven
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Steven Ferry
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Advisory Committee
Role
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internal member
Name
(type = personal)
NamePart
(type = family)
Rong
NamePart
(type = given)
Xiaochun
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Xiaochun Rong
Affiliation
Advisory Committee
Role
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internal member
Name
(type = personal)
NamePart
(type = family)
Futer
NamePart
(type = given)
David
DisplayForm
David Futer
Affiliation
Advisory Committee
Role
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outside member
Name
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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)
This dissertation is based on a joint work with Dr. Julien Roger. We define an associative $mathbb{C}[[h]]$--algebra $AS_h(Sigma)$ generated by framed arcs and links over a punctured surface $Sigma$ which is a quantization of the Poisson algebra $C(Sigma)$ of arcs and curves on $Sigma$. We also construct a Poisson algebra homomorphism from $C(Sigma)$ to the space of smooth functions on the decorated Teichmuller space endowed with the Weil-Petersson Poisson structure. The construction relies on a collection of geodesic lengths identities in hyperbolic geometry which generalizes Penner's Ptolemy relation, the trace identity and Wolpert's cosine formula.
Subject
(authority = RUETD)
Topic
Mathematics
RelatedItem
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TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier
(type = RULIB)
ETD
Identifier
ETD_4600
PhysicalDescription
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electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
vi, 36 p. : ill.
Note
(type = degree)
Ph.D.
Note
(type = bibliography)
Includes bibliographical references
Note
(type = vita)
Includes vita
Note
(type = statement of responsibility)
by Tian Yang
Subject
(authority = ETD-LCSH)
Topic
Low-dimensional topology
Subject
(authority = ETD-LCSH)
Topic
Geometry, Hyperbolic
Subject
(authority = ETD-LCSH)
Topic
Poisson algebras
Identifier
(type = hdl)
http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000069010
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TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
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rucore19991600001
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(displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier
(type = doi)
doi:10.7282/T3183528
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
Yang
GivenName
Tian
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime
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(qualifier = exact);
(point = start)
2013-04-08 15:45:46
AssociatedEntity
Name
Tian Yang
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
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Technical
RULTechMD
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ContentModel
ETD
OperatingSystem
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windows xp
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