On orbifold Gromov–Witten classes

ev : Kg,n(X , d) → ĪX , where ĪX is the rigidified inertia stack of X . See [3, Section 3] for a detailed discussion on inertia stacks and [3, Section 4.4] for the construction of evaluation maps. (2) Forgetting stable maps to X but only retaining the domain curves yields the forgetful map π : Kg,n(X , d) → M tw g,n, where M g,n is the stack of n-pointed genus g orbifold curves, see [19, Theorem 1.9]. Assuming 2g − 2 + n > 0, then passing to coarse curves and stablizing the domains yield another forgetful map p : Kg,n(X , d) → Mg,n, where Mg,n is the stack of n-pointed genus g stable curves. There is an obvious commutative diagram Kg,n(X , d)