Polynomial-time word problems
Group Theory
2007-05-23 v1 Geometric Topology
Abstract
We find polynomial-time solutions to the word problem for free-by-cyclic groups, the word problem for automorphism groups of free groups, and the membership problem for the handlebody subgroup of the mapping class group. All of these results follow from observing that automorphisms of the free group strongly resemble straight line programs, which are widely studied in the theory of compressed data structures. In an effort to be self-contained we give a detailed exposition of the necessary results from computer science.
Cite
@article{arxiv.math/0608563,
title = {Polynomial-time word problems},
author = {Saul Schleimer},
journal= {arXiv preprint arXiv:math/0608563},
year = {2007}
}
Comments
25 pages, 6 figures