Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiplicative formality of operads and Sinha's spectral sequence for
  long knots   Lambrechts, Turchin and Voli\'c proved the Bousfield-Kan type rational
homology spectral sequence associated to the $d$-th Kontsevich operad collapses
at $E^2$-page if $d\geq 4$. The key of their proof is formality of the operad.
In this paper, we simplify their proof using a model category of operads. As
byproducts we obtain two new consequences. One is collapse of the spectral
sequence in the case of $d=3$ (and the coefficients being rational numbers).
The other says there is no non-trivial extension for the Gerstenhaber algebra
structure on the spectral sequence.

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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: econ