Notes on Kontsevich-Soibelman's theorem about cyclic A-infinity algebras

Understand

Kontsevich and Soibelman has proved a relation between a non-degenerate cyclic homology element of an A-infinity algebra A and its cyclic inner products on the minimal model of A.

• We find an explicit formula of this correspondence, in terms of the strong homotopy inner products and negative cyclic cohomology of A.
• We prove that an equivalence class of the induced strong homotopy inner product depends only on the given negative cyclic cohomology class.
• Also, we extend such a correspondence to the case of gapped filtered A-infinity algebras.