Orateur
Chris Brav
Description
We explicate two deformation problems for a smooth Calabi-Yau category C, showing in particular that the complexes underlying the Lie algebras controlling these deformation problems are shifts of negative cyclic and of cylic chains of C. Using these results, we show that the natural map from cyclic chains of C to functions on the `moduli of objects’ M_C is a map of (shifted) Lie algebras with respect to the deformation-theoretic Lie structure on cyclic chains and the Poisson bracket on functions induced by the Calabi-Yau structure on C. Our results give a chain level generalisations of classical constructions of Goldman for moduli of local systems and of Hitchin for GL(n)-Higgs bundles. This is joint work with Nick Rozenblyum.
