| Affiliation: | Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada ; Department of Mathematics, Princeton University, Princeton, New Jersey 08544 ; Department of Mathematics, Royal Institute of Technology, 100 44 Stockholm, Sweden ; Department of Mathematics, Princeton University, Washington Road Fine Hall, Princeton, NJ 08544 |
| 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 of  . 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 of  , and the orbifold quantum cohomology of the symmetric product of  . The results of the paper provide the local Gromov-Witten calculations required for the proofs of these equivalences. |
