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.
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Translated from Funktsional’ nyi Analiz i Ego Prilozheniya, Vol. 45, No. 2, pp. 71–85, 2011
Original Russian Text Copyright © by G. L. Rybnikov
To the blessed memory of I. M. Gelfand
This work was supported in part by RFBR grant no. 09-01-12185-ofi m, by HSE grant no. 09-09-0010, and by HSE project no. TZ-62.0 “Mathematical investigations in small-dimensional topology, algebraic geometry, and representation theory.”
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Rybnikov, G.L. On the fundamental group of the complement of a complex hyperplane arrangement. Funct Anal Its Appl 45, 137–148 (2011). https://doi.org/10.1007/s10688-011-0015-8
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DOI: https://doi.org/10.1007/s10688-011-0015-8