Topological 1D gravity, KP hierarchy, and orbifold Euler characteristics of M‾g,n - Zhiyuan Wang; Jian Zhou (Nuclear Physics B)
In this work we study the tau-function Z1D of the KP hierarchy specified by the topological 1D gravity. As an application, we present two types of algorithms to compute the orbifold Euler characteristics of the moduli spaces M‾g,n of stable curves. The first is to use (fat or thin) topological recursion formulas emerging from the Virasoro constraints for Z1D; and the second is to use a formula for the connected n-point functions of a KP tau-function in terms of its affine coordinates on the Sato Grassmannian. This is a sequel to an earlier work [34].