A Formality quasi-isomorphism for Hochschild cochains over rationals can be constructed recursively
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.
Keywords
Cite
@article{arxiv.1306.6733,
title = {A Formality quasi-isomorphism for Hochschild cochains over rationals can be constructed recursively},
author = {Vasily Dolgushev},
journal= {arXiv preprint arXiv:1306.6733},
year = {2017}
}
Comments
Belatedly to Volodya Rubtsov on the occasion of his 60th birthday. The final version of this paper will appear in International Mathematics Research Notices