Topological Recursion Relations by Localization

Eric Edward Katz

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Topological Recursion Relations by Localization

Eric Edward Katz

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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}.

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Eric Edward Katz. 2012-06-15. Topological Recursion Relations by Localization. https://arxiv.org/abs/math/0310050

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