How to model the free loop space algebraically (Q1298165)

Thanks to the non-commutative algebraic models developed by the authors [\textit{N. Dupont} and \textit{K.Hess}, Math. Ann. 314, No. 3, 449-467 (1999; Zbl 0937.18016)] an explicit model for the free loop space is given. This algebraic model is easily and explicitely described. The cohomology \(H^{*}((S^{n})^{S^1};k)\) of the free loop space of an odd-dimensional sphere \(S^n\) is determined, and also of the free loop space over \(S^{3}\vee S^{3}\).