Topological Recursion Relations by Localization

Abstract

Let M_{g,n} be the moduli space of stable genus g curves with n marked points. M_{g,n} has boundary strata consisting of nodal curves. The fundamental classes of these boundary strata may be linearly dependent in the Chow group A_*(M_{g,n}). Relations among these boundary strata can be found by exploiting a localization trick involving stable maps to P^1. This note explains this trick and applies it to give a new derivation of Getzler's relation among codimension 2 boundary strata in M_{1,4}.