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On the Fundamental Group of the Complement of a Complex Hyperplane Arrangement

G. L. Rybnikov

National Research University "Higher School of Economics"

Abstract: 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.

UDC: 514.14+515.146.27

Received: 11.01.2010

DOI: 10.4213/faa3025

 English version: Functional Analysis and Its Applications, 2011, 45:2, 137–148

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