Orbifold Euler Characteristics of ℳ_g,n [article]

Zhiyuan Wang, Jian Zhou
2021 arXiv   pre-print
We solve the problem of the computation of the orbifold Euler characteristics of _g,n. We take the works of Harer-Zagier and Bini-Harer as our starting point, and apply the formalisms developed in and to this problem. These formalisms are typical examples of mathematical methods inspired by quantum field theories. We also present many closed formulas and some numerical data. In genus zero the results are related to Ramanujan polynomials, and in higher genera we get recursion relations almost
more » ... ntical to the recursion relations for Ramanujan polynomials but with different initial values. We also show that the generating series given by the orbifold Euler characteristics of ℳ_g,n is the logarithm of the KP tau-function of the topological 1D gravity evaluated at the times given by the orbifold Euler characteristics of ℳ_g,n. Conversely, the logarithm of this tau-function evaluated at the times given by certain generating series of the orbifold Euler characteristics of ℳ_g,n is a generating series of the orbifold Euler characteristics of ℳ_g,n. This is a new example of open-closed duality.
arXiv:1812.10638v2 fatcat:zk77f7bcovhkpd6xb4dgeicosq