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Gromov-Witten Axioms for Symplectic Manifolds via Polyfold Theory

  • Author(s): Schmaltz, Wolfgang William
  • Advisor(s): Wehrheim, Katrin
  • et al.
Abstract

Polyfold theory, as developed by Hofer, Wysocki, and Zehnder, is a relatively new approach to resolving transversality issues that arise in the study of J-holomorphic curves in symplectic geometry. This approach has recently led to a well-defined Gromov--Witten invariant for J-holomorphic curves of arbitrary genus, and for all closed symplectic manifolds. In this thesis we prove the Effective, Grading, Homology, Zero, Symmetry, Fundamental Class, and Divisor Gromov--Witten axioms for $J$-holomorphic curves of arbitrary genus, and for all closed symplectic manifolds.

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