Fundamental group of complex hypocycloids-Reference-Cited by-同舟云学术

Fundamental group of complex hypocycloids

Published:2024-07-20 Issue:4 Volume:118 Page:
ISSN:1578-7303
Container-title:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
language:en
Short-container-title:Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.

Author:

Catalán-Ramírez Erich U.^ORCID

Abstract

AbstractThe Zariski–van Kampen theorem allows us to provide a presentation of the fundamental group for the complement of algebraic plane curves. However, certain computations require arduous work, as exemplified in the case of hypocycloids. In this paper we present the following result: Theorem 1.The fundamental group of any complex hypocycloid withNcusps is the Artin group of theN-gon. The main idea of the proof is take advantage of the symmetries inherent in the hypocycloid, allowing us to partition the domain to determine the generators of the fundamental group.

Funder

Consejo Nacional de Ciencia y Tecnología

Publisher

Springer Science and Business Media LLC

Link

https://link.springer.com/content/pdf/10.1007/s13398-024-01644-6.pdf

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