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arXiv · 1705.03268

Wirtinger curves, Artin groups, and hypocycloids

Enrique Artal Bartolo·José Ignacio Cogolludo-Agustín·Jorge Martín-Morales
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Abstract

The computation of the fundamental group of the complement of an algebraic plane curve has been theoretically solved since Zariski-van Kampen, but actual computations are usually cumbersome. In this work, we describe the notion of Wirtinger presentation of such a group relying on the real picture of the curve and with the same combinatorial flavor as the classical Wirtinger presentation; we determine a significant family of curves for which Wirtinger presentation provides the required fundamental group. The above methods allow us to compute that fundamental group for an infinite subfamily of hypocycloids, relating them with Artin groups.

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Enrique Artal Bartolo, José Ignacio Cogolludo-Agustín, Jorge Martín-Morales. 2017-08-31. Wirtinger curves, Artin groups, and hypocycloids. https://doi.org/10.1007/s13398-017-0437-0

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