Titel
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.
Stichwort
group splittingline patternWhitehead graphJSJ-decompositiongeometric word
Objekt-Typ
Sprache
Englisch [eng]
Persistent identifier
https://phaidra.univie.ac.at/o:440201
Erschienen in
Titel
Algebraic & Geometric Topology
Band
16
Ausgabe
2
Seitenanfang
621
Seitenende
673
Verlag
Mathematical Sciences Publishers
Projektnummer
M1717-N25 – Austrian Science Fund (FWF)
Erscheinungsdatum
2016-04-26
Zugänglichkeit

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