2 Sentences With "bouquet of circles"

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Out(Fn) acts geometrically on a cell complex known as Culler–Vogtmann Outer space, which can be thought of as the Teichmüller space for a bouquet of circles.
Any subgroup H of the fundamental group is itself the fundamental group of a connected covering space Y → X. The space Y is a (possibly infinite) topological graph, the Schreier coset graph having one vertex for each coset in G/H., Section 2.2.2, The Subgroup Property, pp. 100–101. In any connected topological graph, it is possible to shrink the edges of a spanning tree of the graph, producing a bouquet of circles that has the same fundamental group H. Since H is the fundamental group of a bouquet of circles, it is itself free.