2013/06/28 by Vasily Dolgushev, Dolgushev, Vasily
Computer Science · Mathematics · #Advanced Algebra and Logic #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Logic, programming, and type systems #Number Theory (math.NT) #Quantum Algebra (math.QA) #math.KT #math.NT #math.QA
paper · pdf · doi:10.48550/arxiv.1306.6733
Belatedly to Volodya Rubtsov on the occasion of his 60th birthday. The final version of this paper will appear in International Mathematics Research Notices
openalex publication_date 2013/06/28 · arxiv created 2017/02/09 · arxiv updated 2017/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.