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arXiv · 1706.09679

A graph-theoretic proof for Whitehead's second free-group algorithm

Warren Dicks
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Abstract

J.H.C. Whitehead's second free-group algorithm determines whether or not two given elements of a free group lie in the same orbit of the automorphism group of the free group. The algorithm involves certain connected graphs, and Whitehead used three-manifold models to prove their connectedness; later, Rapaport and Higgins & Lyndon gave group-theoretic proofs. Combined work of Gersten, Stallings, and Hoare showed that the three-manifold models may be viewed as graphs. We give the direct translation of Whitehead's topological argument into the language of graph theory.

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Warren Dicks. 2017-06-29. A graph-theoretic proof for Whitehead's second free-group algorithm. https://arxiv.org/abs/1706.09679

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