English

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 FF under the automorphisms of FF 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"