Line Patterns in Free Groups
Abstract
We study line patterns in a free group by considering the topology of the decomposition space, a quotient of the boundary at infinity of the free group related to the line pattern. We show that the group of quasi-isometries preserving a line pattern in a free group acts by isometries on a related space if and only if there are no cut pairs in the decomposition space.
Cite
@article{arxiv.1006.2123,
title = {Line Patterns in Free Groups},
author = {Christopher H. Cashen and Natasa Macura},
journal= {arXiv preprint arXiv:1006.2123},
year = {2014}
}
Comments
35 pages, 22 figures, PDFLatex; v2. finite index requires extra hypothesis; v3. 37 pages, 24 figures: updated references and add example in Section 6.3 of a rigid pattern for which the free group is not finite index in the group of pattern preserving quasi-isometries; v4. 40 pages, 26 figures: improved exposition and add example in Section 6.4 of a rigid pattern whose cube complex is not a tree