Geodesic
The Cohomology of Canonical Quotients of Free Groups and Lyndon Words
Documenta mathematica, Tome 22 (2017), pp. 973-997
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For a prime number p and a free profinite group S, let S(n,p) be the nth term of its lower p-central filtration, and S[n,p] the corresponding quotient. Using tools from the combinatorics of words, we construct a canonical basis of the cohomology group H2(S[n,p],Z/p), which we call the Lyndon basis, and use it to obtain structural results on this group. We show a duality between the Lyndon basis and canonical generators of S(n,p)/S(n+1,p). We prove that the cohomology group satisfies shuffle relations, which for small values of n fully describe it.
DOI : 10.4171/dm/584
Classification : 12G05, 20E18, 20J06, 68R15
Mots-clés : Massey products, profinite cohomology, lower p-central filtration, Lyndon words, Shuffle relations 
@article{10_4171_dm_584,
     author = {Ido Efrat},
     title = {The {Cohomology} of {Canonical} {Quotients} of {Free} {Groups} and {Lyndon} {Words}},
     journal = {Documenta mathematica},
     pages = {973--997},
     year = {2017},
     volume = {22},
     doi = {10.4171/dm/584},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/584/}
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Ido Efrat. The Cohomology of Canonical Quotients of Free Groups and Lyndon Words. Documenta mathematica, Tome 22 (2017), pp. 973-997. doi: 10.4171/dm/584

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