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arXiv · 2010.07008

Operadic structure on the Gerstenhaber-Schack complex for prestacks

Hoang Dinh Van·Lander Hermans·Wendy Lowen
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Abstract

We introduce an operad which acts on the Gerstenhaber-Schack complex of a prestack as defined by Dinh Van and Lowen, and which in particular allows us to endow this complex with an underlying $L_{\infty}$-structure. We make use of the operad $\operatorname{Quilt}$ which was used by Hawkins in order to solve the presheaf case. Due to the additional difficulty posed by the presence of twists, we have to use $\operatorname{Quilt}$ in a fundamentally different way (even for presheaves) in order to allow for an extension to prestacks. The resulting $L_{\infty}$-algebra governs the deformation theory of the prestack.

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Hoang Dinh Van, Lander Hermans, Wendy Lowen. 2020-10-14. Operadic structure on the Gerstenhaber-Schack complex for prestacks. https://doi.org/10.1007/s00029-022-00759-1

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