Bouquet of circles
From Wikipedia, the free encyclopedia
In mathematics, a bouquet of circles or rose is a construction in topology occurring when some number of circles are "glued" to each other so that they share a single common point. The number of circles used in the construction may be finite or infinite. It is a special case of the more general wedge sum of pointed topological spaces.
The bouquet of two circles is known as figure-eight space. It has a fundamental group that is a free group in two generators. Thus, for example, the Cayley graph for two generators is the covering space for the figure eight space.
More generally, a bouquet of n circles has a fundamental group that is the free group in n generators. However, this identification does not hold in the direct limit of 
. The bouquet of a countable infinity of circles is known as a Hawaiian earring; its fundamental group is not the free group in a countable infinity of generators.
