Geometry & Topology

Line patterns in free groups

Christopher H Cashen and Nataša Macura

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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.

Article information

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

Dates
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
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
Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]
Secondary: 20E05: Free nonabelian groups

Keywords
free group quasi-isometry rigidity line pattern Whitehead graph Whitehead's Algorithm

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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