Comparing Absolute and relative Gromov--Witten invariants

Abstract

This note compares the usual (absolute) Gromov-Witten invariants of a symplectic manifold with the invariants that count the curves relative to a (symplectic) divisor D. We give explicit examples where these invariants differ even though it seems at first that they should agree, for example when counting genus zero curves in a class \be such that \be\cdot D=0. The main tool is the decomposition formula in the form developed by A. Li--Ruan.

23 pages, 2 figures

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Cited by in corpus (3)

• Symplectic Homology of complements of smooth divisors
• Relative Ruan and Gromov-Taubes Invariants of Symplectic 4-Manifolds
• Positive divisors in symplectic geometry