Clusters, currents and Whitehead's algorithm

Details Clusters, currents and Whitehead's algorithm Clusters, currents and Whitehead's algorithm

2005-11-19

arxiv.org/abs/math/0511478v2

Mathematics

Group Theory

Updated version, to appear in "Experimental Mathematics"

Scientific paper

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.

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