Stable gauged maps

Abstract

We give an introduction to moduli stacks of gauged maps satisfying a stability conditition introduced by Mundet and Schmitt, and the associated integrals giving rise to gauged Gromov-Witten invariants. We survey various applications to cohomological and K-theoretic Gromov-Witten invariants.

Survey for the 2015 AMS Summer Institute on Algebraic Geometry. Split off from the more technical paper "Properness for scaled gauged maps" [arXiv:1606.01383]. There is still substantial overlap between the two papers. This version has minor corrections