Abstract
The local Gromov-Witten theory of curves is solved by localization and degeneration methods. Localization is used for the exact evaluation of basic integrals in the local Gromov-Witten theory ofP1\mathbb P^1. A TQFT formalism is defined via degeneration to capture higher genus curves. Together, the results provide a complete and effective solution. The local Gromov-Witten theory of curves is equivalent to the local Donaldson-Thomas theory of curves, the quantum cohomology of the Hilbert scheme points ofC2\mathbb C^2, and the orbifold quantum cohomology of the symmetric product ofC2\mathbb C^2. The results of the paper provide the local Gromov-Witten calculations required for the proofs of these equivalences.
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