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Topological 1D Gravity, KP Hierarchy, and Orbifold Euler Characteristics of $\overline{\mathcal M}_{g,n}$ (2109.03394v1)
Published 8 Sep 2021 in math-ph, math.MP, and nlin.SI
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 $\overline{\mathcal M}_{g,n}$. 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.