I recently read the original paper by Chas-Sullivan on string topology, in which they introduce some operations on homology of free loopspace LM, where M is a compact oriented manifold, giving it the structure of a (Gerstenhaber-)Batalin-Vilkovisky algebra. However, the arguments in this paper rely on some transversality assumptions, and I'm not sure whether these assumptions are justified. I know that the Chas-Sullivan operations have been constructed via homotopy theoretic methods by Cohen, Jones, Voronov (hopefully I'm not missing any names here), but I am wondering whether anybody has managed to construct the Chas-Sullivan operations in a way that more or less follows the original ideas (e.g. without using any homotopy theory).
I would like to point at the Diploma thesis of my student Lennart Meier, who has given various elementary descriptions of the Chaas Sullivan product (for example using my description of singular homology in terms of bordism groups of stratifolds, see: http://www.hausdorff-research-institute.uni-bonn.de/files/kreck-DA.pdf). I'm sure he will send you an electronic version of his thesis: firstname.lastname@example.org.