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arXiv · 1306.6733

A Formality quasi-isomorphism for Hochschild cochains over rationals can be constructed recursively

Vasily Dolgushev
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Abstract

It is believed arXiv:0808.2762, arXiv:math/9904055 that, among the coefficients entering Kontsevich's formality quasi-isomorphism arXiv:q-alg/9709040, there are irrational (possibly even transcendental) numbers. In this paper, we prove that a formality quasi-isomorphism for Hochschild cochains of a polynomial algebra over rationals can be constructed recursively. The proof that the proposed recursive algorithm works, is based on the existence of formality quasi-isomorphism over reals. However, the algorithm requires no explicit knowledge of the coefficients entering Kontsevich's construction. Although this algorithm completely bypasses Tamarkin's approach arXiv:math/0003052, arXiv:math/9803025, the construction is inspired by Proposition 5.8 from the classical paper (Algebra i Analiz, 1990) by V. Drinfeld.

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Vasily Dolgushev. 2013-06-28. A Formality quasi-isomorphism for Hochschild cochains over rationals can be constructed recursively. https://arxiv.org/abs/1306.6733

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