Resumen de The pure cohomology of multiplicative quiver varieties

Kevin McGerty, Thomas Nevins

• To a quiver Q and choices of nonzero scalars qi, non-negative integers αi, and integers θi labeling each vertex i, Crawley-Boevey–Shaw associate a multiplicative quiver variety Mqθ(α), a trigonometric analogue of the Nakajima quiver variety associated to Q, α, and θ. We prove that the pure cohomology, in the Hodge-theoretic sense, of the stable locus Mqθ(α)s is generated as a Q-algebra by the tautological characteristic classes. In particular, the pure cohomology of genus g twisted character varieties of GLn is generated by tautological classes.