Topological 1D gravity, KP hierarchy, and orbifold Euler characteristics of M‾g,n

Abstract

In this work we study the tau-function $Z^{1D}$ 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 ${\bar{M}}_{g,n}$ of stable curves. The first is to use (fat or thin) topological recursion formulas emerging from the Virasoro constraints for $Z^{1D}$; 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].