Bouquet of circles (${\bigvee }_{i\in I}{S}^1$)

A bouquet of circles identifies one point of each of a family of circles to a common point, using the quotient topology. As a CW complex it has one vertex and one graph loop for each circle. The empty family means a single point. Its fundamental group is the free group on the family, as described by the fundamental group of a bouquet of circles.