On the topology of hypocycloids
arXiv:1703.08308
Abstract
Algebraic geometry has many connections with physics: string theory, enumerative geometry, and mirror symmetry, among others. In particular, within the topological study of algebraic varieties physicists focus on aspects involving symmetry and non-commutativity. In this paper, we study a family of classical algebraic curves, the hypocycloids, which have links to physics via the bifurcation theory. The topology of some of these curves plays an important role in string theory and also appears in Zariski's foundational. We compute the fundamental groups of some of these curves and show that they are in fact Artin groups.
arXiv comment16 pages, 14 figures, In Mathematical physics and field theory. Julio Abad, in memoriam, eds. M. Asorey Carballeira, J.V. García Esteve, Manuel F. Rañada, J. Sesma, ISBN 978-84-92774-04-3; pages 83-98. Prensas Universitarias de Zaragoza, Zaragoza, 2009