2026-09-20T21:59:06Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1018222026-06-17T14:44:55Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Katrin Wehrheim.
Li, Jiayong, Ph. D. Massachusetts Institute of Technology
Massachusetts Institute of Technology. Department of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2016-03-25T13:38:03Z
2016-03-25T13:38:03Z
2015
2015
http://hdl.handle.net/1721.1/101822
941788281
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 253-254).
For 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.
by Jiayong Li.
Ph.D.
254 pages
eng
Massachusetts Institute of Technology
M.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.
http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
A-infinity algebras for Lagrangians via polyfold theory for Morse trees with holomorphic disks
Thesis
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Publication
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<Abstract>For 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.</Abstract>
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