Double ramification cycles on the moduli spaces of admissible covers

TL;DR

This paper derives a formula for the virtual class of moduli spaces of rubber maps to orbifold targets and shows that their Gromov-Witten invariants are determined by existing calculations, advancing understanding in orbifold Gromov-Witten theory.

Contribution

It provides a new formula for the virtual class of rubber maps to orbifold targets and relates their Gromov-Witten theory to known results.

Findings

Derived a formula for the virtual class of rubber maps

Gromov-Witten theory of [P^1/G] is determined by known calculations

Advances understanding of orbifold Gromov-Witten invariants

Abstract

We derive a formula for the virtual class of the moduli space of rubber maps to $[\mathbb{P}^1/G]$ pushed forward to the moduli space of stable maps to $BG$. As an application, we show that the Gromov-Witten theory of $[\mathbb{P}^1/G]$ relative to $0$ and $\infty$ are determined by known calculations.