Higher brackets on cyclic and negative cyclic (co)homology
Abstract
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 e_3-algebra structure on Hochschild cohomology. The results are given in the general and unifying setting of (opposite) cyclic modules over (cyclic) operads.
Cite
@article{arxiv.1712.09717,
title = {Higher brackets on cyclic and negative cyclic (co)homology},
author = {Domenico Fiorenza and Niels Kowalzig},
journal= {arXiv preprint arXiv:1712.09717},
year = {2018}
}
Comments
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