Geodesic
Massey Products and Lower Central Series of Free Groups
Canadian journal of mathematics, Tome 39 (1987) no. 2, pp. 322-337

Voir la notice de l'article provenant de la source Cambridge University Press

The purpose of this paper is to continue the investigation into the relationships amongst Massey products, lower central series of free groups and the free differential calculus (see [4], [9], [12]). In particular we set forth the notion of a universal Massey product ≪α 1, ..., αk ≫, where the αi are one dimensional cohomology classes. This product is defined with zero indeterminacy, natural and multilinear in its variables.In order to state the results we need some notation. Throughout F will denote the free group on fixed generators x 1, ..., xn and will denote the lower central series of F. If I = (i 1, ..., ik ) is a sequence such that 1 ≦ i 1, ..., ik ≦ n then ∂1 is the iterated Fox derivative and , where is the augmentation. By convention we set ∂1 = identity if I is empty. 
Fenn, Roger; Sjerve, Denis. Massey Products and Lower Central Series of Free Groups. Canadian journal of mathematics, Tome 39 (1987) no. 2, pp. 322-337. doi: 10.4153/CJM-1987-015-5
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[1] 1. Dwyer, , Homology, Massey products and maps between groups. Journal of Pure and Applied Algebra 6 (1975), 177–190. Google Scholar

[2] 2. Dyer-Vasquez, , Some small aspherical spaces, Jour. Australian Math. Soc. 16 (1973), 332–352. Google Scholar

[3] 3. Fenn-Sjerve, , Duality and cohomology for one relator groups, Pacific J. Math. 103 (1982), 365–375. Google Scholar

[4] 4. Fenn-Sjerve, , Basic commutators and minimal Massey products, Can. J. Math. 36 (1984), 1119–1146. Google Scholar

[5] 5. Labute, , Classification of Demushkin groups, Can. J. Math. 19 (1967), 106–121. Google Scholar

[6] 6. Lyndon, , Cohomology theory of groups with a single defining relation, Annals of Math. 52 (1950), 650–665. Google Scholar

[7] 7. MacLane, , Homology (Springer-Verlag, 1963). Google Scholar | DOI

[8] 8. May, , Matric Massey products, Jour. Alg. 12 (1969), 533–568. Google Scholar

[9] 9. Porter, , Milnor's -invariants and Massey products, T.A.M.S. 257 (1980), 39–71. Google Scholar

[10] 10. Ratcliffe, , On one relator groups which satisfy Poincaré duality, Math. Z. 177 (1981), 425–438. Google Scholar

[11] 11. Shapiro-Sonn, , Free factor groups of one relator groups, Duke Math. J. 41 (1974), 83–88. Google Scholar

[12] 12. Turaev, , The Milnor invariants and Massey products, Studies in Topology II, Zap. Nanc. Sem. Lenin. Of. Mat. Kogo in Stet. Acad. Nauk SSSR 66 (1976), 189–203. Google Scholar

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