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The equivariant Gromov-Witten theory of P^1
Andrei Okounkov, Rahul Pandharipande
We express all equivariant Gromov-Witten invariants of the projective line as matrix elements of explicit operators acting in the Fock space. As a consequence, we prove the equivar…
Multipoint series of Gromov-Witten invariants of CP^1
Ezra Getzler, Andrei Okounkov, Rahul Pandharipande
We give explicit formulas for the multipoint series of Gromov-Witten invariants of CP^1. We use the recursions of the Toda hierarchy to calculate these in degree 0, and the Toda eq…
Gromov-Witten theory, Hurwitz theory, and completed cycles
Andrei Okounkov, Rahul Pandharipande
We establish an explicit equivalence between the stationary sector of the Gromov-Witten theory of a target curve X and the enumeration of Hurwitz coverings of X in the basis of com…