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A Comparison Theorem for Gromov-Witten Invariants in the Symplectic Category
In this paper we exploit the geometric approach to the virtual fundamental
class, due to Fukaya-Ono and Li-Tian, to compare the virtual fundamental
classes of stable maps to a symplectic manifold and a symplectic submanifold
whenever all constrained stable maps to the former are contained in the latter
to first order. This extends versions of a statement well-known in the
algebraic category to the symplectic category, where it appears to be less
familiar. The latter's inherent flexibility then leads to a confirmation of
Pandharipande's Gopakumar-Vafa prediction for GW-invariants of Fano classes in
6-dimensional symplectic manifolds. In a forthcoming paper, we use a similar
approach to relative Gromov-Witten invariants and the absolute/relative
correspondence in genus~0.Comment: 29 page
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