Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
Niels Kowalzig (Università di Napoli Federico II)
In this talk, we will embed the degree -d bracket on the equivariant homology of loop spaces developed by Chas-Sullivan and Menichi on negative cyclic cohomology groups as well as the dual bracket found by de Thanhoffer de Voelcsey-Van den Bergh on negative cyclic homology groups (which are the right receptacle for the Chern character coming from algebraic K-theory) into the global picture of a noncommutative differential (or Cartan) calculus on the cyclic bicomplex in general, in case a certain Poincare' duality is given. For negative cyclic cohomology, this in particular leads to a Gerstenhaber algebra structure with generating operator, that is, a Batalin-Vilkovisky algebra structure on the underlying Hochschild cohomology. In the special case in which this BV bracket vanishes, one obtains a graded Lie bracket of degree -2 on Hochschild cohomology.
(joint work with D. Fiorenza)