Open Access
January, 2020 Cocycles of nilpotent quotients of free groups
Takefumi NOSAKA
J. Math. Soc. Japan 72(1): 171-184 (January, 2020). DOI: 10.2969/jmsj/79997999


We focus on the cohomology of the $k$-th nilpotent quotient of a free group. We describe all the group 2-, 3-cocycles in terms of the Massey product and give expressions for some of the 3-cocycles. We also give simple proofs of some of the results on the Milnor invariant and Johnson–Morita homomorphisms.


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Takefumi NOSAKA. "Cocycles of nilpotent quotients of free groups." J. Math. Soc. Japan 72 (1) 171 - 184, January, 2020.


Received: 3 March 2018; Revised: 15 September 2018; Published: January, 2020
First available in Project Euclid: 18 March 2019

zbMATH: 07196502
MathSciNet: MR4055094
Digital Object Identifier: 10.2969/jmsj/79997999

Primary: 20F18 , 20J06 , 55S30
Secondary: 20F14 , 57Q45

Keywords: Group cohomology , higher Massey product , link , mapping class group , nilpotent group

Rights: Copyright © 2020 Mathematical Society of Japan

Vol.72 • No. 1 • January, 2020
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