A new cohomology class on the moduli space of curves

被引：17

作者：

Norbury, Paul ^{[1
]}

机构：

[1] Univ Melbourne, Sch Math & Stat, Melbourne, Vic, Australia

来源：

GEOMETRY & TOPOLOGY | 2023年 / 27卷 / 07期

关键词：

GROMOV-WITTEN INVARIANTS; TOPOLOGICAL RECURSION; INTERSECTION THEORY;

D O I：

10.2140/gt.2023.27.2695

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We define a collection Theta(g,n) is an element of H4g-4 ((M) over bar (g,n), Q) for 2g - 2 + n> 0 of cohomology classes that restrict naturally to boundary divisors. We prove that the intersection numbers integral(M) over bar (g,n), Theta(g,n) Pi(n)(i=1) psi(mi)(i) can be recursively calculated. We conjecture that a generating function for these intersection numbers is a tau function of the KdV hierarchy. This is analogous to the conjecture of Witten proven by Kontsevich that a generating function for the intersection numbers integral(M) over bar (g,n), Theta(g,n) Pi(n)(i=1) psi(mi)(i) is a tau function of the KdV hierarchy.

引用

页码：2695 / 2761

页数：67