Wirtinger curves, Artin groups, and hypocycloids

Artal Bartolo, E. (Universidad de Zaragoza) ; Cogolludo-Agustín, J.I. (Universidad de Zaragoza) ; Martín-Morales, J.

Resumen: 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.

Idioma: Inglés

DOI: 10.1007/s13398-017-0437-0

Año: 2018

Publicado en: Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas 112, 3 (2018), 641-656
ISSN: 1578-7303

Factor impacto JCR: 1.028 (2018)

Categ. JCR: MATHEMATICS rank: 87 / 313 = 0.278 (2018) - Q2 - T1

Factor impacto SCIMAGO: 0.565 - Algebra and Number Theory (Q2) - Analysis (Q2) - Geometry and Topology (Q2) - Computational Mathematics (Q2) - Applied Mathematics (Q2)

Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2016-76868-C2-2-P

Tipo y forma: Artículo (PostPrint)

Área (Departamento): Área Geometría y Topología (Dpto. Matemáticas)