Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01vh53wz90q
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dc.contributor.authorSwaminathan, Mohan
dc.contributor.otherMathematics Department
dc.date.accessioned2022-06-16T20:33:27Z-
dc.date.available2022-06-16T20:33:27Z-
dc.date.created2022-01-01
dc.date.issued2022
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/dsp01vh53wz90q-
dc.description.abstractIn this thesis, we present new results on three aspects of moduli spaces of pseudoholomorphic curves: smoothness, compactness and bifurcations.In the first part of this thesis, dealing with smoothness, we give a functorial construction of a so-called relative smooth structure on the moduli spaces of solutions to the (perturbed) pseudo-holomorphic curve equation. In the second part of this thesis, dealing with compactness, we prove a quantitative version of Gromov’s compactness theorem for closed pseudo-holomorphic curves of genus 0 in a symplectic manifold. In the third part of this thesis, dealing with bifurcations, we study moduli spaces of embedded pseudo-holomorphic curves in a Calabi–Yau 3-fold. Performing a careful bifurcation analysis of these moduli spaces in generic 1-parameter families leads, in some cases, to the construction of an integer valued invariant of Calabi–Yau 3-folds which counts embedded curves with suitably defined integer weights. This part is joint with Shaoyun Bai.
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.publisherPrinceton, NJ : Princeton University
dc.relation.isformatofThe Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog: <a href=http://catalog.princeton.edu>catalog.princeton.edu</a>
dc.subjectGromov-Witten
dc.subjectHolomorphic curve
dc.subjectSymplectic topology
dc.subject.classificationMathematics
dc.subject.classificationTheoretical mathematics
dc.titleNew results in the analysis of pseudo-holomorphic curves