Line patterns in free groups

Cashen, Christopher H¹ ; Macura, Nataša²

¹ Department of Mathematics, University of Utah, 155 S 1400 E Room 233, Salt Lake City UT 84112-0090, USA
² Department of Mathematics, Trinity University, San Antonio TX 78212, USA

Geometry & topology, Tome 15 (2011) no. 3, pp. 1419-1475.

Résumé

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.

Détail

DOI : 10.2140/gt.2011.15.1419

Classification : 20F65, 20E05
Keywords: free group, quasi-isometry, rigidity, line pattern, Whitehead graph, Whitehead's Algorithm

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