Equivariant Gromov-Witten theory of one dimensional stacks

TL;DR

This paper extends the operator formalism for equivariant Gromov-Witten theory from the projective line to orbifold lines, confirming the 2-Toda hierarchy in the effective case and verifying the decomposition conjecture in the ineffective case.

Contribution

It generalizes the operator formalism to orbifold lines and verifies the decomposition conjecture, expanding understanding of Gromov-Witten theory for one-dimensional stacks.

Findings

The theory remains governed by the 2-Toda hierarchy in the effective case.

The decomposition conjecture is verified in the ineffective case.

Extension of formalism to orbifold lines enhances computational methods.

Abstract

In math.AG/0207233, Okounkov and Pandharipande gave an operator formalism for computing the equivariant Gromov-Witten theory of the projective line. This thesis extends their result to orbifold lines. In the effective case the theory is again governed by the 2-Toda hierarchy. In the ineffective case the decomposition conjecture of hep-th/0606034 is verified.