Line patterns in free groups

Christopher H Cashen; Nataša Macura

doi:10.2140/gt.2011.15.1419

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Home > Journals > Geom. Topol. > Volume 15 > Issue 3 > Article

2011 Line patterns in free groups

Christopher H Cashen, Nataša Macura

Geom. Topol. 15(3): 1419-1475 (2011). DOI: 10.2140/gt.2011.15.1419

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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. We also give an algorithm to detect such cut pairs.