Equivariant GromovWitten theory of orbifold curves
Equivariant GromovWitten theory of orbifold curves

P. Johnson, University of Michigan
Fine Hall 214
Consider a $P^1$ with effective orbifold structure at $0$ and $\infty$. We show that that the equivariant GromovWitten theory of such an orbifold is governed by the 2Toda 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 GromovWitten theory is governed by commuting copies of the 2Toda hierarchy, and the symmetric group is replaced by wreath products.