2010/09/30 by Christopher H. Cashen, Christopher H Cashen
Mathematics · #Boundary (topology) #Conjugacy class #Finite Group Theory Research #Geometric and Algebraic Topology #Graph #Group (periodic table) #Homotopy and Cohomology in Algebraic Topology #Line (geometry) #Quotient #Quotient group #Simplicial complex #Tree (set theory) #math.GR #msc:20E05 #msc:20E06 #msc:20F65 #msc:20F67 #msc:57M05
paper · pdf · doi:10.2140/agt.2016.16.621
published as Algebr. Geom. Topol. 16 (2016) 621-673 · 22 pages, 6 figures; v2 fixed a few typos; v3 38 pages, 21 figures; v4 30 pages, 11 figures 'Preliminaries' section expanded to make paper self-contained and split into two sections. Some arguments refactored and simplified. Paper streamlined; v5 56 pages, 21 figures Added examples and improved exposition according to referee comments. To appear in Algebraic & Geometric Topology
arxiv created 2016/01/13 · openalex publication_date 2016/04/26 · arxiv updated 2016/05/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.