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arXiv · 1610.04879

When can a formality quasi-isomorphism over rationals be constructed recursively?

V. A. Dolgushev·G. E. Schneider
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Abstract

Let $O$ be a differential graded (possibly colored) operad defined over rationals. Let us assume that there exists a zig-zag of quasi-isomorphisms connecting $O \otimes K$ to its cohomology, where $K$ is any field extension of rationals. We show that for a large class of such dg operads, a formality quasi-isomorphism for $O$ exists and can be constructed recursively. Every step of our recursive procedure involves a solution of a finite dimensional linear system and it requires no explicit knowledge about the zig-zag of quasi-isomorphisms connecting $O \otimes K$ to its cohomology.

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V. A. Dolgushev, G. E. Schneider. 2016-10-16. When can a formality quasi-isomorphism over rationals be constructed recursively?. https://arxiv.org/abs/1610.04879

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