Twisted orbifold Gromov-Witten invariants

TL;DR

This paper introduces a generalized framework for twisted orbifold Gromov-Witten invariants of smooth Deligne-Mumford stacks, expressing their generating series in relation to untwisted invariants and applying these results to quantum K-theory.

Contribution

It extends the concept of twisted orbifold Gromov-Witten invariants beyond previous definitions and relates their generating series to untwisted invariants, facilitating applications in quantum K-theory.

Findings

Derived formulas relating twisted and untwisted invariants

Expressed generating series of twisted invariants in terms of untwisted series

Provided tools for quantum K-theory computations

Abstract

Let $\ix$ be a smooth Deligne-Mumford stack over the complex numbers. One can define twisted orbifold Gromov-Witten invariants of $\ix$ by considering multiplicative invertible characteristic classes of various bundles on the moduli spaces of stable maps $\ix_{g,n,d}$, cupping them with evaluation and cotangent line classes and then integrating against the virtual fundamental class. These are more general than the twisted invariants introduced by Tseng. We express the generating series of the twisted invariants in terms of the generating series of the untwisted ones. We derive the corollaries which are used in the work of Givental-Tonita on the quantum K-theory of a complex manifold X.