On the Refined Symplectic Sum Formula for Gromov-Witten Invariants
Mohammad F. Tehrani, Aleksey Zinger
TL;DR
This paper refines the symplectic sum formula for Gromov-Witten invariants using abelian covers, providing sharper results and applications such as vanishing theorems.
Contribution
It introduces a refined product operation for Gromov-Witten invariants based on abelian covers, enhancing the symplectic sum formula's precision.
Findings
Refinement sharpens the symplectic sum formula.
Application of the refinement leads to vanishing results.
Provides a topological perspective on the invariants.
Abstract
We describe the extent to which Ionel-Parker's proposed refinement of the standard relative Gromov-Witten invariants sharpens the usual symplectic sum formula. The key product operation on the target spaces for the refined invariants is specified in terms of abelian covers of symplectic divisors, making it suitable for studying from a topological perspective. We give several qualitative applications of this refinement, which include vanishing results for Gromov-Witten invariants.
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