Clusters, currents and Whitehead's algorithm
Group Theory
2007-05-23 v2 Geometric Topology
Abstract
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 under the automorphisms of form "clusters" that share similar normalized Whitehead graphs and similar behavior with respect to Whitehead's algorithm.
Cite
@article{arxiv.math/0511478,
title = {Clusters, currents and Whitehead's algorithm},
author = {Ilya Kapovich},
journal= {arXiv preprint arXiv:math/0511478},
year = {2007}
}
Comments
Updated version, to appear in "Experimental Mathematics"