The string coproduct is a coproduct on the homology with field coefficients of the free loop space of a closed oriented manifold introduced by Sullivan in string topology. The coproduct and the Chas-Sullivan loop product give an infinitesimal bialgebra structure on the homology if the Euler characteristic is zero. The aim of this paper is to study the string coproduct using Sullivan models in rational homotopy theory. In particular, we give a rational model for the string coproduct of pure manifolds. Moreover, we study the behavior of the string coproduct in terms of the Hodge decomposition of the rational cohomology of the free loop space. We also give computational examples of the coproduct rationally.

弦余积是与 Sullivan 在弦拓扑中引入的封闭定向流形的自由环空间的场系数同调的余积。如果欧拉特征为零，则余积和 Chas-Sullivan 环积在同调上给出一个无穷小的双代数结构。本文的目的是使用有理同伦理论中的 Sullivan 模型研究弦余积。特别是，我们给出了纯流形的弦联积的合理模型。此外，我们根据自由环空间的有理上同调的霍奇分解来研究弦余积的行为。我们还合理地给出了联积的计算示例。