## Geometry & Topology

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

#### Article information

Source
Geom. Topol., Volume 15, Number 3 (2011), 1419-1475.

Dates
Revised: 1 June 2011
Accepted: 29 June 2011
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732336

Digital Object Identifier
doi:10.2140/gt.2011.15.1419

Mathematical Reviews number (MathSciNet)
MR2825316

Zentralblatt MATH identifier
1272.20046

Subjects
Secondary: 20E05: Free nonabelian groups

#### Citation

Cashen, Christopher H; Macura, Nataša. Line patterns in free groups. Geom. Topol. 15 (2011), no. 3, 1419--1475. doi:10.2140/gt.2011.15.1419. https://projecteuclid.org/euclid.gt/1513732336

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