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Refined Convergence for Genus-Two Pseudo-Holomorphic Maps

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dc.contributor.advisor Zinger, Aleksey en_US
dc.contributor.author Niu, Jingchen en_US
dc.contributor.other Department of Mathematics en_US
dc.date.accessioned 2017-09-20T16:50:08Z
dc.date.available 2017-09-20T16:50:08Z
dc.date.issued 2016-12-01 en_US
dc.identifier.uri http://hdl.handle.net/11401/76380 en_US
dc.description 87 pgs en_US
dc.description.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. en_US
dc.description.sponsorship This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. en_US
dc.format Monograph en_US
dc.format.medium Electronic Resource en_US
dc.language.iso en_US en_US
dc.publisher The Graduate School, Stony Brook University: Stony Brook, NY. en_US
dc.subject.lcsh Mathematics en_US
dc.title Refined Convergence for Genus-Two Pseudo-Holomorphic Maps en_US
dc.type Dissertation en_US
dc.mimetype Application/PDF en_US
dc.contributor.committeemember Starr, Jason en_US
dc.contributor.committeemember Plamenevskaya, Olga en_US
dc.contributor.committeemember Rocek, Martin en_US

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