I recently read the original paper by ChasSullivan 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)BatalinVilkovisky 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 ChasSullivan 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 ChasSullivan operations in a way that more or less follows the original ideas (e.g. without using any homotopy theory).
Take the 2minute tour
×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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.hausdorffresearchinstitute.unibonn.de/files/kreckDA.pdf). I'm sure he will send you an electronic version of his thesis: lennart@meierbielefeld.de. Matthias Kreck 


I think this was one of the main motivations for the following paper of McClure. math/0410450 On the chainlevel intersection pairing for PL manifolds. J. E. McClure. Geom. Topol. 10 (2006) 13911424 and Geom. Topol. 13 (2009) 17751777. math.QA (math.GT). 

