I was reading John D.S. Jones' paper "Cyclic homology and equivariant homology" where he introduces a variant of cyclic homology that is isomorphic (as modules over the ring $K[u]$) to equivariant homology of the loop space of a simply connected space with the $S^1$ action on the loops, which is what I mean by String Homology.


I have seen how the loop homology BV operator shows up in Hochschild homology. Do we have an analog of string topology operations, such as the string bracket, in cyclic homology?



Are there analogs of String Homology structure in cyclic homology?
Yes, definitively, for example you can look at (my choices are completely arbitrary, I am sorry I am sure to forget plenty of very good references):


* Menichi's paper:
<http://math.univ-angers.fr/perso/lmenichi/BV_cyclic_Hopf_algebra.pdf>
corollary 1.7
* Abbaspour, Tradler and Zeinalian:
<http://xxx.lanl.gov/abs/0807.2351>


it's all about duality and the way you move operations from Hochschild homology to cyclic homology via the Connes'operator.


The situation in the algebraic context of cyclic homology is as rich as the one first described by Moira chas and Dennis Sullivan in string topology see for example (part III) for the geometric story :


<http://arxiv.org/abs/0710.4141>


