This dissertation describes a polyfold approach to the construction of an integration
theory on moduli spaces of pseudo-holomorphic curves with Lagrangian boundary conditions.
Polyfold theory was introduced by Hofer, Wysocki, and Zehnder in a series
of articles. Polyfolds have been employed to study closed Gromov-Witten theory and
Symplectic Field Theory. From its initial introduction, polyfold theory has seen generalizations
which have allowed for a recyclable and modular construction of moduli spaces
arising in symplectic geometry.
The present work sets the beginning of a geometric realization of the theory of Lagrangian
Floer theory in all genera, generalizing the work of Fukaya, Oh, Ohta, and Ono. Similarly
to the construction of Lagrangian Floer theory, construction of Lagrangian Floer theory
in all genera separates into two pieces:
1. The construction of an integration theory on the moduli spaces of pseudo-holomorphic
maps with Lagrangian boundary conditions
2. An ordered perturbation scheme on these moduli spaces which relates geometry (in
particular integration) along the boundary of a given moduli space in terms of geometry
of moduli spaces of lower order
The present article treats the first of these pieces. The second piece is left to subsequent
|Commitee:||Oszvath, Peter, Szabo, Zoltan, Dafermos, Mihalis|
|School Location:||United States -- New Jersey|
|Source:||DAI-B 81/8(E), Dissertation Abstracts International|
|Keywords:||Higher genus, Lagrangian boundary, Lagrangian floer theory, Polyfolds, Symplectic geometry|
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