Calabi-Yau Deformations and Negative Cyclic Homology

Details Calabi-Yau Deformations and Negative Cyclic Homology Calabi-Yau Deformations and Negative Cyclic Homology

2012-01-06

arxiv.org/abs/1201.1520v3

Mathematics

Rings and Algebras

30 pages. Clumsy formulation of Lemma 12.6 changed

Scientific paper

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 $(T^poly[[u]],-u div)$.

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