000131270 001__ 131270 000131270 005__ 20240219135520.0 000131270 0247_ $$2doi$$a10.1007/s13398-017-0437-0 000131270 0248_ $$2sideral$$a107093 000131270 037__ $$aART-2018-107093 000131270 041__ $$aeng 000131270 100__ $$0(orcid)0000-0002-8276-5116$$aArtal Bartolo, E.$$uUniversidad de Zaragoza 000131270 245__ $$aWirtinger curves, Artin groups, and hypocycloids 000131270 260__ $$c2018 000131270 5060_ $$aAccess copy available to the general public$$fUnrestricted 000131270 5203_ $$aThe 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. 000131270 536__ $$9info:eu-repo/grantAgreement/ES/MICINN/MTM2016-76868-C2-2-P 000131270 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000131270 590__ $$a1.028$$b2018 000131270 591__ $$aMATHEMATICS$$b87 / 313 = 0.278$$c2018$$dQ2$$eT1 000131270 592__ $$a0.565$$b2018 000131270 593__ $$aAlgebra and Number Theory$$c2018$$dQ2 000131270 593__ $$aAnalysis$$c2018$$dQ2 000131270 593__ $$aGeometry and Topology$$c2018$$dQ2 000131270 593__ $$aComputational Mathematics$$c2018$$dQ2 000131270 593__ $$aApplied Mathematics$$c2018$$dQ2 000131270 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000131270 700__ $$0(orcid)0000-0003-1820-6755$$aCogolludo-Agustín, J.I.$$uUniversidad de Zaragoza 000131270 700__ $$0(orcid)0000-0002-6559-4722$$aMartín-Morales, J. 000131270 7102_ $$12006$$2440$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Geometría y Topología 000131270 773__ $$g112, 3 (2018), 641-656$$pRev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat.$$tRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas$$x1578-7303 000131270 8564_ $$s515094$$uhttps://zaguan.unizar.es/record/131270/files/texto_completo.pdf$$yPostprint 000131270 8564_ $$s1629352$$uhttps://zaguan.unizar.es/record/131270/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000131270 909CO $$ooai:zaguan.unizar.es:131270$$particulos$$pdriver 000131270 951__ $$a2024-02-19-13:51:22 000131270 980__ $$aARTICLE