Geometry & Topology
- Geom. Topol.
- Volume 15, Number 3 (2011), 1419-1475.
Line patterns in free groups
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.
Geom. Topol., Volume 15, Number 3 (2011), 1419-1475.
Received: 8 September 2010
Revised: 1 June 2011
Accepted: 29 June 2011
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]
Secondary: 20E05: Free nonabelian groups
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