P. Johnson

Equivariant Gromov-Witten theory of orbifold curves

Consider a P^1 with effective orbifold structure at 0 and infinity. We show that that the equivariant Gromov-Witten theory of such an orbifold is governed by the 2-Toda hierarchy. The proof follows that of Okounkov and Pandharipande for the case of a smooth P^1, and goes through Hurwitz numbers and the representation theory of the symmetric group. In the case of an ineffective orbifold, the Gromov-Witten theory is governed by commuting copies of the 2-Toda hierarchy, and the symmetric group is replaced by wreath products.