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The multiplihedra in Lagrangian Floer theory
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Title
The multiplihedra in Lagrangian Floer theory
Name
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Mau
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Sikimeti Luisa
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Sikimeti Luisa Mau
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author
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Woodward
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Chris
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Advisory Committee
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Chris Woodward
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chair
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Weibel
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Charles
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Advisory Committee
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Charles Weibel
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Buch
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Anders
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Advisory Committee
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Anders Buch
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Albers
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Peter
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Advisory Committee
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Peter Albers
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Rutgers University
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Graduate School - New Brunswick
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theses
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2008
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2008-10
Language
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English
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electronic
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vi, 173 pages
Abstract
We apply the quilted Floer theory of Wehrheim and Woodward to families of quilted surfaces parametrized by the Stasheff multiplihedra. Our approach is modeled on the construction of the Fukaya category, which applies Floer theory to families of pointed Riemann surfaces parametrized by the associahedra. First, we show that the multiplihedra are realized as a moduli space of quilted disks. Using the quilted disks we define the moduli space of pseudoholomorphic quilted disks, which under suitable transversality assumptions are smooth manifolds. Then we prove a gluing theorem relating ``broken'' tuples of pseudoholomorphic quilted disks with boundaries of one-parameter familes of pseudoholomorphic quilted disks.
Note
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Ph.D.
Note
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Includes bibliographical references (p. 171-172).
Subject
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Topic
Mathematics
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Topic
Geometry, Differential
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Graduate School - New Brunswick Electronic Theses and Dissertations
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rucore19991600001
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http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.17526
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ETD_1322
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NjNbRU
Identifier
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doi:10.7282/T31N81F7
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ETD doctoral
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Rights
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The author owns the copyright to this work.
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Copyright protected
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Open
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Name
Sikimeti Mau
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Affiliation
Rutgers University. Graduate School - New Brunswick
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Non-exclusive ETD license
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Author Agreement License
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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.
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