Open Access
April 2015 Multiplicative formality of operads and Sinha’s spectral sequence for long knots
Syunji Moriya
Kyoto J. Math. 55(1): 17-27 (April 2015). DOI: 10.1215/21562261-2801858


Lambrechts, Turchin, and Volić proved the Bousfield–Kan-type rational homology spectral sequence associated to the dth Kontsevich operad collapses at E2-page if d4. 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 d=3 (and the coefficients being rational numbers). The other says there is no nontrivial extension for the Gerstenhaber algebra structure on the spectral sequence.


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Syunji Moriya. "Multiplicative formality of operads and Sinha’s spectral sequence for long knots." Kyoto J. Math. 55 (1) 17 - 27, April 2015.


Published: April 2015
First available in Project Euclid: 13 March 2015

zbMATH: 1312.55018
MathSciNet: MR3323525
Digital Object Identifier: 10.1215/21562261-2801858

Primary: 55U35

Rights: Copyright © 2015 Kyoto University

Vol.55 • No. 1 • April 2015
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