Type
Text
Type
Dissertation
Advisor
Zinger, Aleksey | Starr, Jason | Plamenevskaya, Olga | Rocek, Martin.
Date
2016-12-01
Keywords
Mathematics
Department
Department of Mathematics
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/76380
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
The moduli spaces of pseudo-holomorphic maps into an almost Kahler manifold are fundamental to Gromov-Witten theory. It has been speculated since the early days of Gromov-Witten theory that these moduli spaces contain natural closed subspaces, whenever the genus is positive, that also give rise to curve-counting invariants. This speculation was confirmed in genus 1 over a decade ago. In this dissertation, we describe a natural subspace of every moduli space of genus 2 pseudo-holomorphic maps that has strata of the correct virtual dimension to give rise to curve-counting invariants. We establish most of the convergence statements for sequences of such maps needed to show that this subspace is closed. | 87 pages
Recommended Citation
Niu, Jingchen, "Refined Convergence for Genus-Two Pseudo-Holomorphic Maps" (2016). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 2304.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/2304