上海科技大学知识管理系统

For an S1-framed modular operad P, we introduce its “Feynman com-pactification" denoted by FP which is a modular operad. Let {Mfr(g, n)}(g,n) be the S1-framed modular operad defined using moduli spaces of smooth curves with framings along punctures. We prove that the homology operad of FMfr is isomor-phic to H∗((SCI)), the homology operad of the Deligne-Mumford operad. Using this isomorphism, we obtain an explicit formula of the fundamental class of [(SIC)g,n/Sn] in terms of Sen-Zwiebach’s string vertices. As an immediate application, we prove Costello’s categorical enumerative invariants of the ground field match with the Gromov-Witten invariants of a point.