A Deligne conjecture for prestacks
| Autor: | Campos, Ricardo, Hermans, Lander |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We prove an analog of the Deligne conjecture for prestacks. We show that given a prestack $\mathbb A$, its Gerstenhaber--Schack complex $\mathbf{C}_{\mathsf{GS}}(\mathbb A)$ is naturally an $E_2$-algebra. This structure generalises both the known $\mathsf{L}_\infty$-algebra structure on $\mathbf{C}_{\mathsf{GS}}(\mathbb A)$, as well as the Gerstenhaber algebra structure on its cohomology $\mathbf{H}_{\mathsf{GS}}(\mathbb A)$. The main ingredient is the proof of a conjecture of Hawkins \cite{hawkins}, stating that the homology of the dg operad $\mathsf{Quilt}$ has vanishing homology in positive degrees. As a corollary, $\Quilt$ is quasi-isomorphic to the operad $\mathsf{Brace}$ encoding brace algebras. In addition, we improve the $L_\infty$-structure on $\Quilt$ be showing that it originates from a $\mathsf{PreLie}_\infty$-structure lifting the $\mathsf{PreLie}$-structure on $\mathsf{Brace}$ in homology. Comment: Comments are welcome |
| Databáze: | arXiv |
| Externí odkaz: |
|