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arXiv · 1712.09717

Higher brackets on cyclic and negative cyclic (co)homology

Domenico Fiorenza·Niels Kowalzig
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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.

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BibTeXRIS

Domenico Fiorenza, Niels Kowalzig. 2018-09-26. Higher brackets on cyclic and negative cyclic (co)homology. https://arxiv.org/abs/1712.09717

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