Virtual cycles of gauged Witten equation
  We construct virtual cycles on moduli spaces of perturbed gauged Witten equation over a fixed smooth r -spin curve, under the framework of [TX15]. Together with the wall-crossing formula proved in the companion paper [TX19], it completes the construction of the correlation function for the gauged linear sigma model announced in [TX16] as well as the proof of its invariance. 
Gang Tian, Guangbo Xu
math.SG math-ph math.MP