A-infinity algebras for Lagrangians via polyfold theory for Morse trees with holomorphic disks
Name
941788281-MIT.pdf
Description
Full printable version
Size
12.57 MB
Format
Adobe PDF
Checksum (MD5)
c91205133740fcc770c64fac2332e4bb
Author(s)
Li, Jiayong, Ph. D. Massachusetts Institute of Technology
Advisor(s)
Katrin Wehrheim.
Date Issued
2015
Publisher
Massachusetts Institute of Technology
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.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 253-254).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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.
Persistent DSpace Link
