Journal of Noncommutative Geometry


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Volume 8, Issue 3, 2014, pp. 655–693
DOI: 10.4171/JNCG/167

Published online: 2014-09-15

Crossed interval groups and operations on the Hochschild cohomology

Michael A. Batanin[1] and Martin Markl[2]

(1) Macquarie University, Sydney, Australia
(2) Czech Academy of Sciences, Prague

We prove that the operad $\mathcal{B}$ of natural operations on the Hochschild cohomology has the homotopy type of the operad of singular chains on the little disks operad. To achieve this goal, we introduce crossed interval groups and show that $\mathcal{B}$ is a certain crossed interval extension of an operad $\mathcal{T}$ whose homotopy type is known. This completes the investigation of the algebraic structure on the Hochschild cochain complex that has lasted for several decades.

Keywords: Crossed interval group, Hochschild cohomology, natural operation

Batanin Michael, Markl Martin: Crossed interval groups and operations on the Hochschild cohomology. J. Noncommut. Geom. 8 (2014), 655-693. doi: 10.4171/JNCG/167