Abstract
Lambrechts, Turchin, and Volić proved the Bousfield–Kan-type rational homology spectral sequence associated to the th Kontsevich operad collapses at -page if . The key of their proof is formality of the operad. In this paper, we simplify their proof by using a model category of operads. As by-products we obtain two new consequences. One is collapse of the spectral sequence in the case of (and the coefficients being rational numbers). The other says there is no nontrivial extension for the Gerstenhaber algebra structure on the spectral sequence.
Citation
Syunji Moriya. "Multiplicative formality of operads and Sinha’s spectral sequence for long knots." Kyoto J. Math. 55 (1) 17 - 27, April 2015. https://doi.org/10.1215/21562261-2801858
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