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dc.contributor.advisorKatrin Wehrheim.en_US
dc.contributor.authorLi, Jiayong, Ph. D. Massachusetts Institute of Technologyen_US
dc.contributor.otherMassachusetts Institute of Technology. Department of Mathematics.en_US
dc.date.accessioned2016-03-25T13:38:03Z
dc.date.available2016-03-25T13:38:03Z
dc.date.copyright2015en_US
dc.date.issued2015en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/101822
dc.descriptionThesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015.en_US
dc.descriptionCataloged from PDF version of thesis.en_US
dc.descriptionIncludes bibliographical references (pages 253-254).en_US
dc.description.abstractFor a Lagrangian submanifold, we define a moduli space of trees of holomorphic disk maps with Morse flow lines as edges, and construct an ambient space around it which we call the quotient space of disk trees. We show that this ambient space is an M-polyfold with boundary and corners by combining the infinite dimensional analysis in sc-Banach space with the finite dimensional analysis in Deligne-Mumford space. We then show that the Cauchy-Riemann section is sc-Fredholm, and by applying the polyfold perturbation we construct an A[infinity]. algebra over Z₂ coefficients. Under certain assumptions, we prove the invariance of this algebra with respect to choices of almost-complex structures.en_US
dc.description.statementofresponsibilityby Jiayong Li.en_US
dc.format.extent254 pagesen_US
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsM.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582en_US
dc.subjectMathematics.en_US
dc.titleA-infinity algebras for Lagrangians via polyfold theory for Morse trees with holomorphic disksen_US
dc.typeThesisen_US
dc.description.degreePh. D.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematics.en_US
dc.identifier.oclc941788281en_US


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