Journal of the Mathematical Society of Japan

Cocycles of nilpotent quotients of free groups

Takefumi NOSAKA

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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.

Article information

J. Math. Soc. Japan, Volume 72, Number 1 (2020), 171-184.

Received: 3 March 2018
Revised: 15 September 2018
First available in Project Euclid: 18 March 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55S30: Massey products 20F18: Nilpotent groups [See also 20D15] 20J06: Cohomology of groups
Secondary: 57Q45: Knots and links (in high dimensions) {For the low-dimensional case, see 57M25} 20F14: Derived series, central series, and generalizations

nilpotent group higher Massey product group cohomology mapping class group link


NOSAKA, Takefumi. Cocycles of nilpotent quotients of free groups. J. Math. Soc. Japan 72 (2020), no. 1, 171--184. doi:10.2969/jmsj/79997999.

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