Abstract
Based on Johnson's operator formula for the equivariant Gromov-Witten theory of P1-orbifolds, we give a new approach to the operator formalism by Okounkov and Pandharipande regarding the C⁎-equivariant Gromov-Witten theory of P1 relative to one or two points. We also extend their operator formalism in the non-equivariant specialization to the case where we allow negative contact orders.
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