Splittings of free groups, normal forms and partitions of ends
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Splittings of a free group correspond to embedded spheres in the 3-manifold M = # k S 2 × S 1. These can be represented in a normal form due to Hatcher. In this paper, we determine the normal form in terms of crossings of partitions of ends corresponding to normal spheres, using a graph of trees representation for normal forms. In particular, we give a constructive proof of a criterion determining when a conjugacy class in π 2(M) can be represented by an embedded sphere.
KeywordsFree groups sphere complex algebraic intersection numbers graphs of trees
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