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 Volcsey-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-Vilkoviski (BV) algebra structure on the underlying Hochschild cohomology. In the special case in which this BV bracket vanishes, one obtains an -algebra structure on Hochschild cohomology. The results are given in the general and unifying setting of (opposite) cyclic modules over (cyclic) operads.

Fiorenza, D., Kowalzig, N. (2020). Higher brackets on cyclic and negative cyclic (co)homology. INTERNATIONAL MATHEMATICS RESEARCH NOTICES(23), 9148-9209 [10.1093/imrn/rny241].

Higher brackets on cyclic and negative cyclic (co)homology

Kowalzig, N
2020-01-01

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 Volcsey-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-Vilkoviski (BV) algebra structure on the underlying Hochschild cohomology. In the special case in which this BV bracket vanishes, one obtains an -algebra structure on Hochschild cohomology. The results are given in the general and unifying setting of (opposite) cyclic modules over (cyclic) operads.
2020
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/02 - ALGEBRA
English
Fiorenza, D., Kowalzig, N. (2020). Higher brackets on cyclic and negative cyclic (co)homology. INTERNATIONAL MATHEMATICS RESEARCH NOTICES(23), 9148-9209 [10.1093/imrn/rny241].
Fiorenza, D; Kowalzig, N
Articolo su rivista
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/313905
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 6
  • ???jsp.display-item.citation.isi??? 5
social impact