Clusters, Currents, and Whitehead's Algorithm
Kapovich, Ilya
Experiment. Math., Tome 16 (2007) no. 1, p. 67-76 / Harvested from Project Euclid
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Using geodesic currents, we provide a theoretical justification for some of the experimental results obtained by Haralick, Miasnikov, and Myasnikov via pattern-recognition methods regarding the behavior of Whitehead's algorithm on nonminimal inputs. 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.
Publié le : 2007-05-14
Classification:  Whitehead's algorithm,  geodesic currents,  free groups,  genericity,  20F36,  20E36 
@article{1175789802,
     author = {Kapovich, Ilya},
     title = {Clusters, Currents, and Whitehead's Algorithm},
     journal = {Experiment. Math.},
     volume = {16},
     number = {1},
     year = {2007},
     pages = { 67-76},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1175789802}
}

Kapovich, Ilya. Clusters, Currents, and Whitehead's Algorithm. Experiment. Math., Tome 16 (2007) no. 1, pp.  67-76. http://gdmltest.u-ga.fr/item/1175789802/