Localization, cobordism, and twisted $χ_y$-genera of $\overline{\mathcal{M}}_{0,n}$

We use the method of equivariant localization to obtain a recursion for the cobordism-valued one-point psi-class intersections on $\overline{\mathcal{M}}_{0,n}$, and hence the cobordism classes $[\overline{\mathcal{M}}_{0,n}]$. Restricting to the hyperbolic formal group law, we recover the Poincaré polynomials of $\overline{\mathcal{M}}_{0,n}$ as a special case, and obtain new formulas for Hirzebruch $χ_y$-genera of $\overline{\mathcal{M}}_{0,n}$ twisted by tautological line bundles.