Erratum to: "A Proof of Tsygan's Formality Conjecture for an Arbitrary Smooth Manifold"

Vasiliy A. Dolgushev

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Erratum to: "A Proof of Tsygan's Formality Conjecture for an Arbitrary Smooth Manifold"

Vasiliy A. Dolgushev

Quantum Algebra · Submitted 4 Mar 2007

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The correction does not change the results of math.QA/0504420.

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arXiv IDmath/0703113 (version 1)

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CitationVasiliy A. Dolgushev. "Erratum to: "A Proof of Tsygan's Formality Conjecture for an Arbitrary Smooth Manifold"." arXiv:math/0703113 (2007). https://pith.science/paper/Z2XNJJWF

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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,906 input tokens.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.35 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.30 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Boris Shoikhet noticed that the proof of lemma 1 in section 2.3 of math.QA/0504420 contains an error. In this note I give a correct proof of this lemma which was suggested to me by Dmitry Tamarkin. The correction does not change the results of math.QA/0504420.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Boris Shoikhet noticed that the proof of lemma 1 in section 2.3 of math.QA/0504420 contains an error.	background 0.94	0.11	0.10	asserted 1.00
s1	In this note I give a correct proof of this lemma which was suggested to me by Dmitry Tamarkin.	contribution 1.00	0.87	0.35	asserted 1.00
s2	The correction does not change the results of math.QA/0504420.	result 0.66	0.59	0.46	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.72 · evidence from proof or derivation 0.99.

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arXiv listing abstract v1

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

Boris Shoikhet noticed that the proof of lemma 1 in section 2.3 of math.QA/0504420 contains an error. In this note I give a correct proof of this lemma which was suggested to me by Dmitry Tamarkin. The correction does not change the results of math.QA/0504420.

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References

How the literature uses it

12 arXiv papers cite this in 28 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 20 sentences without a confident label

Contests it 1 paper

(In [ref] , this circumstance is ignored, and a $t$-dependent element $x$ is obtained, which thus does not literally provide a gauge homotopy).

A tale of three homotopies · Quillen homotopy and gauge homotopy · contest 0.84

Uses its method or tool 2 papers

More precisely, in [ref] a chain homotopy is constructed which contracts the complex $((M, C^+1()), D + ^)$ to its sub-DGLA [equation] Using this chain homotopy and [ref] , one constructs an $$ quasi-isomorphism [equation] satisfying two properties: first, all the structure maps $_n$ of $$ take values in the sub-DGLA ([ref]); second, $$ is homotopy equivalent to the composition [equation] Composing $$ with the inverse of the isomorphism [ref] we get the desired $$ quasi-isomorphism $$ ([ref]).

Morita equivalence and characteristic classes of star products · A sequence of quasi-isomorphisms between $^+1(M)$ and $(_M)$ · 0.92
If this coboundary term is non-zero then applying Lemma 1 from [ref] we modify the $$ quasi-isomorphism ([ref]) in such a way that $F_1$ will coincide with ([ref]).

Formality theorems for Hochschild complexes and their applications · An example of a non-formal DG Lie algebra · 0.89

Cites it as support 1 paper

By [ref] we know that $𝒰^B ∘τ∘ν^-1$ and $U$ are homotopic.

The Homotopy Class of twisted $L_\infty$-morphisms · Preliminaries: Globalization Procedure · 0.97

Cites it as background 2 papers

Application of these $L_∞$-gauge symmetries to studying homotopies between morphisms of $L_∞$-algebras goes back to [ref] .

A tale of three homotopies · Gauge homotopy · 0.80
Further details can be found in Sections 2.3 and 2.4 in [ref] and in [ref] .

Morita equivalence and characteristic classes of star products · Maurer-Cartan elements and the twisting procedure · 1.00

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