Non-homotopicity of the linking set of algebraic plane curves

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  • Benoît Guerville-Ballé
    Department of Mathematics, Tokyo Gakugei University, Koganei-shi, Tokyo 184-8501, Japan
  • Taketo Shirane
    National Institute of Technology, Ube College, 2-14-1 Tokiwadai, Ube 755-8555, Yamaguchi, Japan

Description

<jats:p> The linking set is an invariant of algebraic plane curves introduced by Meilhan and the first author. It has been successfully used to detect several examples of Zariski pairs, i.e. curves with the same combinatorics and different embedding in [Formula: see text]. Differentiating Shimada's [Formula: see text]-equivalent Zariski pair by the linking set, we prove, in the present paper, that this invariant is not determined by the fundamental group of the curve. </jats:p>

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