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Gravity formality

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We show that Willwacher’s cyclic formality theorem can be extended to preserve natural Gravity operations on cyclic multivector fields and cyclic multidifferential operators. We express this in terms of a… Click to show full abstract

We show that Willwacher’s cyclic formality theorem can be extended to preserve natural Gravity operations on cyclic multivector fields and cyclic multidifferential operators. We express this in terms of a homotopy Gravity quasi-isomorphism with explicit local formulas. For this, we develop operadic tools related to mixed complexes and cyclic homology and prove that the operad M of natural operations on cyclic operators is formal and hence quasi-isomorphic to the Gravity operad.

Keywords: gravity; gravity formality; formality

Journal Title: Advances in Mathematics
Year Published: 2018

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