Crossed interval groups and operations on the Hochschild cohomology

Details Crossed interval groups and operations on the Hochschild cohomology Crossed interval groups and operations on the Hochschild cohomology

2008-03-14

arxiv.org/abs/0803.2249v3

Mathematics

Algebraic Topology

34 pages. The distinction between the normalized and unital versions of the operad of natural operations made clear

Scientific paper

We prove that the operad 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 B is a certain crossed interval extension of an operad 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.

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