Clusters, currents and Whitehead's algorithm

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.
Updated version, to appear in "Experimental Mathematics"

Keywords

Group Theory, Geometric Topology, 20F

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/104993

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0511478
 http://arxiv.org/abs/math/0511478

Collections

arXiv