Geodesic
On the Fundamental Group of the Complement of a Complex Hyperplane Arrangement
Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 2, pp. 71-85

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We construct two combinatorially equivalent line arrangements in the complex projective plane such that the fundamental groups of their complements are not isomorphic. The proof uses a new invariant of the fundamental group of the complement to a line arrangement of a given combinatorial type with respect to isomorphisms inducing the canonical isomorphism of the first homology groups.
Keywords: hyperplane arrangement, matroid, homology groups, fundamental group, lower central series. 
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     title = {On the {Fundamental} {Group} of the {Complement} of a {Complex} {Hyperplane} {Arrangement}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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G. L. Rybnikov. On the Fundamental Group of the Complement of a Complex Hyperplane Arrangement. Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 2, pp. 71-85. http://geodesic.mathdoc.fr/item/FAA_2011_45_2_a4/