Title
Splitting line patterns in free groups
Abstract
We construct a boundary of a finite-rank free group relative to a finite list of conjugacy classes of maximal cyclic subgroups. From the cut points and uncrossed cut pairs of this boundary, we construct a simplicial tree on which the group acts cocompactly. We show that the quotient graph of groups is the JSJ decomposition of the group relative to the given collection of conjugacy classes. This provides a characterization of virtually geometric multiwords: they are the multiwords that are built from geometric pieces. In particular, a multiword is virtually geometric if and only if the relative boundary is planar.
Keywords
group splittingline patternWhitehead graphJSJ-decompositiongeometric word
Object type
Language
English [eng]
Persistent identifier
https://phaidra.univie.ac.at/o:440201
Appeared in
Title
Algebraic & Geometric Topology
Volume
16
Issue
2
From page
621
To page
673
Publisher
Mathematical Sciences Publishers
Date issued
2016-04-26
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