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arXiv:math/0511478 [math.GR]AbstractReferencesReviewsResources

Clusters, currents and Whitehead's algorithm

Ilya Kapovich

Published 2005-11-19, updated 2006-09-12Version 2

Using geodesic currents, we provide a theoretical justification for some of the experimental results regarding the behavior of Whitehead's algorithm on non-minimal inputs, that were obtained by Haralick, Miasnikov and Myasnikov via pattern recognition methods. In particular we prove that the images of "random" elements of a free group $F$ under the automorphisms of $F$ form "clusters" that share similar normalized Whitehead graphs and similar behavior with respect to Whitehead's algorithm.

Comments: Updated version, to appear in "Experimental Mathematics"
Categories: math.GR, math.GT
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