Topological 1D Gravity, KP Hierarchy, and Orbifold Euler Characteristics of $\overline{\mathcal M}_{g,n}$
Mathematical Physics
2021-09-09 v1 math.MP
Exactly Solvable and Integrable Systems
Abstract
In this work we study the tau-function 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 first is to use (fat or thin) topological recursion formulas emerging from the Virasoro constraints for ; and the second is to use a formula for the connected -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.
Keywords
Cite
@article{arxiv.2109.03394,
title = {Topological 1D Gravity, KP Hierarchy, and Orbifold Euler Characteristics of $\overline{\mathcal M}_{g,n}$},
author = {Zhiyuan Wang and Jian Zhou},
journal= {arXiv preprint arXiv:2109.03394},
year = {2021}
}