A genus-4 topological recursion relation for Gromov-Witten invariants

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In this paper,we give a new genus-4 topological recursion relation for Gromov-Witten invariants of compact symplectic manifolds via Pixton\'s relations on the moduli space of curves.As an application,we prove that Pixton\'s relations imply a known topological recursion relation on(M)g,1 for genus g≤4.
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