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Line patterns in free
groups
Christopher H Cashen and Nataša Macura |
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Geometry & Topology 15 (2011) 1419–1475
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 20E05
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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
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Authors |
| Christopher H Cashen | |
| Department of Mathematics University of Utah 155 S 1400 E Room 233 Salt Lake City UT 84112-0090 USA |
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| http://www.math.utah.edu/~cashen | |
| Nataša Macura | |
| Department of Mathematics Trinity University San Antonio TX 78212 USA |
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| http://www.trinity.edu/nmacura | |
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