Journal of the Mathematical Society of Japan

Cocycles of nilpotent quotients of free groups

Takefumi NOSAKA

Abstract

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

Source
J. Math. Soc. Japan, Advance publication (2019), 14 pages.

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

https://projecteuclid.org/euclid.jmsj/1552896022

Digital Object Identifier
doi:10.2969/jmsj/79997999

Citation

NOSAKA, Takefumi. Cocycles of nilpotent quotients of free groups. J. Math. Soc. Japan, advance publication, 18 March 2019. doi:10.2969/jmsj/79997999. https://projecteuclid.org/euclid.jmsj/1552896022

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