Frobenius有理Loop代数
Frobenius Rational Loop Algebra
摘要：
最近R。Cohen和V. Godin证明了域中系数的闭定向流形的自由闭路空间的同调具有无可数的Frobenius代数的结构。本文证明了当域的特征为零且流形为1-连通时，代数结构仅取决于流形的有理同伦类型。我们建立了一个代数模型，并用它来做一些计算。
英文摘要：
Recently R. Cohen and V. Godin have proved that the homology of the free loop space of a closed oriented manifold with coefficients in a field has the structure of a Frobenius algebra without counit. In this short note we prove that when the characteristic of the field is zero and when the manifold is 1-connected the algebraic structure depends only on the rational homotopy type of the manifold. We build an algebraic model and use it to do some computations.
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