Calabi–Yau deformations and negative cyclic homology

  • Louis de Thanhoffer de Völcsey

    University of Toronto at Scarborough, Canada
  • Michel Van den Bergh

    Universiteit Hasselt, Diepenbeek, Belgium


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 .

Cite this article

Louis de Thanhoffer de Völcsey, Michel Van den Bergh, Calabi–Yau deformations and negative cyclic homology. J. Noncommut. Geom. 12 (2018), no. 4, pp. 1255–1291

DOI 10.4171/JNCG/304