A-infinity algebras for Lagrangians via polyfold theory for Morse trees with holomorphic disks
Author(s)Li, Jiayong, Ph. D. Massachusetts Institute of Technology
Massachusetts Institute of Technology. Department of Mathematics.
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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.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015.Cataloged from PDF version of thesis.Includes bibliographical references (pages 253-254).
DepartmentMassachusetts Institute of Technology. Department of Mathematics.
Massachusetts Institute of Technology