2017/12/28 by Domenico Fiorenza, Fiorenza, Domenico, Niels Kowalzig +1 · 1 citation
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA) #math.AT #math.KT #math.QA
paper · pdf · doi:10.48550/arxiv.1712.09717
40 pages; v2: Theorem 5.7 now proven without any assumption on the morphism j; v3: minor revision, to appear in Int. Math. Res. Not
arxiv created 2018/09/26 · arxiv updated 2018/09/27
The purpose of this article is to embed the string topology bracket 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 into the global picture of a noncommutative differential (or Cartan) calculus up to homotopy on the (co)cyclic bicomplex in general, in case a certain Poincare' duality is given. For negative cyclic cohomology, this in particular leads to a Batalin-Vilkovisky algebra structure on the underlying Hochschild cohomology. In the special case in which this BV bracket vanishes, one obtains an e3-algebra structure on Hochschild cohomology. The results are given in the general and unifying setting of (opposite) cyclic modules over (cyclic) operads.