131270 20240219135520.0 doi 10.1007/s13398-017-0437-0 sideral 107093 ART-2018-107093 eng Artal Bartolo, E. Universidad de Zaragoza (orcid)0000-0002-8276-5116 Wirtinger curves, Artin groups, and hypocycloids 2018 Access copy available to the general public Unrestricted 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. info:eu-repo/grantAgreement/ES/MICINN/MTM2016-76868-C2-2-P info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 1.028 2018 MATHEMATICS 87 / 313 = 0.278 2018 Q2 T1 0.565 2018 Algebra and Number Theory 2018 Q2 Analysis 2018 Q2 Geometry and Topology 2018 Q2 Computational Mathematics 2018 Q2 Applied Mathematics 2018 Q2 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Cogolludo-Agustín, J.I. Universidad de Zaragoza (orcid)0000-0003-1820-6755 Martín-Morales, J. (orcid)0000-0002-6559-4722 2006 440 Universidad de Zaragoza Dpto. Matemáticas Área Geometría y Topología 112, 3 (2018), 641-656 Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas 1578-7303 515094 http://zaguan.unizar.es/record/131270/files/texto_completo.pdf Postprint 1629352 http://zaguan.unizar.es/record/131270/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:131270 articulos driver 2024-02-19-13:51:22 ARTICLE