The Gauss–Manin connection on the periodic cyclic homology

  title={The Gauss–Manin connection on the periodic cyclic homology},
  author={Alexander Petrov and Dmitry Vaintrob and V. Vologodsky},
  journal={Selecta Mathematica},
AbstractLet R be the algebra of functions on a smooth affine irreducible curve S over a field k and let $${A_{\bullet }}$$A∙ be a smooth and proper DG algebra over R. The relative periodic cyclic homology $$HP_* ({A_{\bullet }})$$HP∗(A∙) of $${A_{\bullet }}$$A∙ over R is equipped with the Hodge filtration $${\mathcal F}^{\cdot }$$F· and the Gauss–Manin connection $$\nabla $$∇ (Getzler, in: Quantum deformations of algebras and their representations (Ramat-Gan, 1991/1992; Rehovot, 1991/1992… Expand
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