Volume 15, issue 3 (2011)

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Line patterns in free groups

Christopher H Cashen and Nataša Macura

Geometry & Topology 15 (2011) 1419–1475
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.

Keywords
free group, quasi-isometry, rigidity, line pattern, Whitehead graph, Whitehead's Algorithm
Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 20E05
References
Publication
Received: 8 September 2010
Revised: 1 June 2011
Accepted: 29 June 2011
Published: 1 August 2011
Proposed: Walter Neumann
Seconded: Joan Birman, Colin Rourke
Authors
Christopher H Cashen
Department of Mathematics
University of Utah
155 S 1400 E Room 233
Salt Lake City UT 84112-0090
USA
http://www.math.utah.edu/~cashen
Nataša Macura
Department of Mathematics
Trinity University
San Antonio TX 78212
USA
http://www.trinity.edu/nmacura