Properties of Gromov-Witten invariants defined via global Kuranishi charts
Abstract
Using the global Kuranishi charts constructed in HS22, we define gravitational descendants and equivariant Gromov-Witten invariants for general symplectic manifolds. We prove that that these invariants, equivariant and non-equivariant, satisfy the axioms of Kontsevich and Manin and their generalisations. A virtual localisation formula holds in this setting; we use it derive an explicit formula for the equivariant GW invariants of a class of Hamiltonian manifolds. A comparison with the GW invariants of RT97 is given in the semipositive case.
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