Acyclicity conjecture for the Quilt operad

Let Quilt\operatorname{\textit{Quilt}} be the operad of quilts, and let Hk(Quilt)H_k(\operatorname{Quilt}) denote its homology in degree kk. Acyclicity conjecture for the Quilt operad. Quilt\operatorname{\textit{Quilt}} is acyclic in the sense that

Hk(Quilt)=0H_k(\operatorname{\textit{Quilt}})=0

for every k>0k>0. This conjecture concerns the homological structure of the operad governing operations on the Hochschild bicomplex of a diagram of algebras. The supplied text gives no evidence that the claim has been resolved.

Sources & referencesView supporting material

Primary source

Eli Hawkins, “Operations on the Hochschild Bicomplex of a Diagram of Algebras”, arXiv:2002.00886 (2024).

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