3 research outputs found
Hyperbolic surface subgroups of one-ended doubles of free groups
Gromov asked whether every one-ended word-hyperbolic group contains a
hyperbolic surface group. We prove that every one-ended double of a free group
has a hyperbolic surface subgroup if (1) the free group has rank two, or (2)
every generator is used the same number of times in the amalgamating words. To
prove this, we formulate a stronger statement on Whitehead graphs and prove its
specialization by combinatorial induction for (1) and the characterization of
perfect matching polytopes by Edmonds for (2).Comment: 30 pages, 8 figures. This version has been accepted for publication
by the Journal of Topolog