  In this paper we relate the deformation theory of Ginzburg Calabi-Yau
algebras to negative cyclic homology. We do this by exhibiting a DG-Lie algebra
that controls this deformation theory and whose homology is negative cyclic
homology. We show that the bracket induced on negative cyclic homology
coincides with Menichi's string topology bracket. We show in addition that the
obstructions against deforming Calabi-Yau algebras are annihilated by the map
to periodic cyclic homology.
  In the commutative we show that our DG-Lie algebra is homotopy equivalent to
$(T^{\operatorname{poly}}[[u]],-u \operatorname{div})$.
