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A fine property of Whitehead's algorithm

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Publication:6381061

DOI10.4171/GGD/746arXiv2110.11936OpenAlexW3209486374MaRDI QIDQ6381061

Author name not available (Why is that?)

Publication date: 22 October 2021

Abstract: We develop a refinement of Whitehead's algorithm for primitive words in a free group. We generalize to subgroups, establishing a strengthened version of Whitehead's algorithm for free factors. We make use of these refinements in proving new results about primitive elements and free factors in a free group. These include a relative version of Whitehead's algorithm, and a criterion that tests whether a subgroup is a free factor just by looking at its primitive elements. We develop an algorithm to determine whether or not two vertices in the free factor complex have distance d for d=1,2,3, as well as d=4 in a special case.


Full work available at URL: https://doi.org/10.4171/ggd/746




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