Volume 16, issue 2 (2016)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Splitting line patterns in free groups

Christopher H Cashen

Algebraic & Geometric Topology 16 (2016) 621–673
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 splitting, line pattern, Whitehead graph, JSJ-decomposition, geometric word, virtually geometric multiword, relatively hyperbolic group, free group
Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 57M05, 20E05
References
Publication
Received: 30 September 2010
Revised: 26 December 2015
Accepted: 12 January 2016
Published: 26 April 2016
Authors
Christopher H Cashen
Fakultät Für Mathematik
Universität Wien
Oskar-Morgenstern-Platz 1
1090 Wien
Österreich
http://www.mat.univie.ac.at/~cashen