A-infinity algebras for Lagrangians via polyfold theory for Morse trees with holomorphic disks

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2015

Author dc:creator

• Li, Jiayong, Ph. D. Massachusetts Institute of Technology

Advisor dc:contributor.advisor

• Katrin Wehrheim.

• Mathematics.

Statement dc:rights

• 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/101822

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/101822