Cocycles of nilpotent quotients of free groups
Takefumi Nosaka
TL;DR
This paper investigates the cohomology of nilpotent quotients of free groups, expressing cocycles via Massey products and connecting to Milnor invariants and Johnson-Morita homomorphisms.
Contribution
It provides explicit descriptions of 2- and 3-cocycles in nilpotent quotients and offers simplified proofs of related invariants and homomorphisms.
Findings
All 2- and 3-cocycles described in terms of Massey products
Expressions for certain 3-cocycles provided
Simplified proofs of Milnor invariants and Johnson-Morita homomorphisms
Abstract
We focus on the cohomology of the -th nilpotent quotient of the free group, . This paper describes all the group 2-, 3-cocycles in terms of Massey products, and gives expressions for some of the 3-cocycles. We also give simple proofs of some of the results on Milnor invariants and the Johnson-Morita homomorphisms.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory