Whitehead's algorithm for free groups and the free factor complex

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• Dario Ascari (University of Oxford)
• Friday 04 March 2022, 13:45-14:45
• Zoom.

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The classical Whitehead’s algorithm allows, given an element of a free group, to determine whether or not the element is part of some basis for the free group. This has been proved, generalized and applied in several ways along the years; we discuss some results, both old and new.

We introduce the complex of free factors of a free group; this is naturally acted on by the group of automorphisms of the free group. This is the analogous for free groups of what the curve complex is for surfaces; but despite the curve complex is quite well understood, the free factor complex remains more mysterious.

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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