TITLE: String topology for a Lie group  
QUESTION [6 upvotes]: My question is very naive maybe, I don't have a deep knowledge about string topology. I wanted to ask (explanation or a reference) for the geometric interpretation 
of free loop space (continues maps) $\mathrm{Map}(S^{1}, G)$, when G is a topological group (Lie group). Does it classify something geometric? 
Thank you.

REPLY [4 votes]: The free loop space sits in a fibration
$$
\Omega M \to M^{S^1} \to M
$$
and in the case where $M = G$ is a Lie-group, I understand the main point of Richard Hepworths paper http://arxiv.org/abs/0905.1199 as saying that the fibration trivializes to a product $G^{S^1} \cong G \times \Omega G$. This triviality then makes it more evident how the string topology operations is a mixture of the two geometric entities: the intersection product of $\mathbb{H}_*(G)$ and the $E_1$-structure on the based loops $\Omega G$.