A van Kampen theorem for equivariant fundamental groupoids

• Autores: Manuel Bullejos Lorenzo , Laura Scull
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 212, Nº 9, 2008, págs. 2059-2068
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2007.12.005
• Texto completo no disponible (Saber más ...)
• Resumen

  • The equivariant fundamental groupoid of a G-space X is a category which generalizes the fundamental groupoid of a space to the equivariant setting. In this paper, we prove a van Kampen theorem for these categories: the equivariant fundamental groupoid of X can be obtained as a pushout of the categories associated to two open G-subsets covering X. This is proved by interpreting the equivariant fundamental groupoid as a Grothendieck semidirect product construction, and combining general properties of this construction with the ordinary (non-equivariant) van Kampen theorem. We then illustrate applications of this theorem by showing that the equivariant fundamental groupoid of a G-CW complex only depends on the 2-skeleton and also by using the theorem to compute an example.