Line Patterns in Free Groups

Details Line Patterns in Free Groups Line Patterns in Free Groups

2010-06-10

arxiv.org/abs/1006.2123v4

Geom. Topol. 15 (2011), no. 3, 1419--1475

Mathematics

Group Theory

35 pages, 22 figures, PDFLatex; v2. finite index requires extra hypothesis; v3. 37 pages, 24 figures: updated references and a

Scientific paper

10.2140/gt.2011.15.1419

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.

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